Despite the emphatic nature of the final score it was Burnley who started and finished the brighter of the two teams.
But for all Burnley's early endeavour it was the Hammers who scored first.
Moments after seeing Franco head against the bar the home side took the lead through the impressive Collison.
The Welshman beat the offside trap to latch on to Parker's quickly taken free-kick before slotting underneath Jensen from 12 yards out.
Franco's endeavour up front was a problem for the visitors throughout the first half and the Mexican was unlucky to see his header fly just over the bar.
Zola relieved to take three points
West Ham continued to press and late into the half they doubled their lead.
It came from Stanislas, who broke the Burnley offside line to latch on to Franco's intelligent pass and while his first shot was saved from Jensen, he found the net from a tight angle via the far post with the rebound.
And Burnley's first half misery increased just before the break with Cole finding the net from the penalty spot - his seventh league goal of the season - after Robbie Blake had brought down the marauding Jonathan Spector.
The Hammers brought on Zavon Hines at the break for Cole - who had been injured earlier in the game after a collision with Jensen - and they soon increased their lead.
It came from Franco who headed Stanislas's free-kick from the right flank past Jensen from six yards out for 4-0.
Collison scored West Ham's opener on Saturday
In an attempt to get back into the game Burnley brought on David Nugent but the striker wasted two golden opportunities in quick succession.
But it was the substitution of Jimenez for Franco that made the more meaningful impact.
Parker was allowed too much space in midfield and he found Jimenez with a defence-splitting pass but as he latched on to the ball he was brought down by the onrushing Jensen.
Jimenez picked himself up to slot home the penalty but just as the Hammers pressed for a sixth, Burnley grabbed a lifeline.
Eagles, who was one of Burnley's better performers on the day, found room on the left and his shot across goal was tapped home at the far post by Fletcher.
The goal sparked life into the Clarets, who soon after made it 5-2 with a goal that was almost a carbon copy of the first.
Coyle takes lessons from loss
Eagles again found space on the left, and after working his way into the box he crossed for Fletcher at the far post who slotted under Green and into the net.
The former Manchester United winger then hit the post with a 25-yard free-kick as Burnley sensed an opportunity to get back into the match.
Late on Caldwell was red carded for hauling down Hines but Burnley scored again with Eagles side-footing Tyrone Mears's cross from just inside the box.
But despite late pressure the Hammers held out to secure only their second home win of the season.
West Ham manager Gianfranco Zola: "It was an entertaining game, although I would have preferred to have conceded fewer goals - but you can't have everything.
"Right now we are very good coming forward, we just need to keep the balance when we are defending. We switched off too early. But we wanted the three points today, and we have to be happy with that.
"I will take a lot of positives from this game - we scored another five goals. Going forwards we are doing very well."
Burnley boss Owen Coyle: "We were the architects of our own downfall.
"We gifted some soft goals, and made individual errors at the wrong time.
"I am loath to criticise officials, because I know how difficult the job is, but there were some big decisions which went against us, like on the second goal when Franco controlled the ball with his arm. Is the third a penalty? I don't know.
90:00+5:17 The referee signals the end of the game.
90:00+4:19 Assist on the goal came from Tyrone Mears.
90:00+4:19 GOAL - Chris Eagles:West Ham 5 - 3 Burnley Chris Eagles scores a goal from inside the area low into the middle of the goal. West Ham 5-3 Burnley.
90:00+2:07 Junior Stanislas has an effort direct from the free kick, blocked by Christian Kalvenes. Jonathan Spector has a shot on goal
from outside the box which misses right.
90:00+2:07 Booking The referee cautions Brian Jensen for dissent.
90:00+1:36 Sent off Steven Caldwell is sent off by the referee for professional foul.
90:00+1:26 Steven Caldwell challenges Zavon Hines unfairly and gives away a free kick.
90:00+0:15 Steven Fletcher takes a shot. Daniel Gabbidon gets a block in.
89:32 Andre Bikey takes a shot. Save by Robert Green.
86:50 Junior Stanislas takes a shot. Comfortable save by Brian Jensen.
83:54 Tyrone Mears restarts play with the free kick.
83:54 Booking Herita Ilunga goes into the referee's book for unsporting behaviour.
83:50 Herita Ilunga gives away a free kick for an unfair challenge on Wade Elliott.
83:32 Zavon Hines concedes a free kick for a foul on Chris Eagles. Brian Jensen restarts play with the free kick.
81:39 Christian Kalvenes challenges Zavon Hines unfairly and gives away a free kick. Manuel Da Costa takes the direct free kick.
79:27 Unfair challenge on Steven Fletcher by Scott Parker results in a free kick. Shot on goal comes in from Chris Eagles from the
77:42 The referee blows for offside. Clarke Carlisle takes the direct free kick.
76:11 Substitution (West Ham) makes a substitution, with Julien Faubert coming on for Jack Collison.
76:11 Corner taken by Chris Eagles from the right by-line, Headed effort from inside the area by Andre Bikey misses to the left
of the target.
75:05 Wade Elliott takes a shot. Blocked by Daniel Gabbidon.
73:44 Chris Eagles provided the assist for the goal.
73:44 GOAL - Steven Fletcher:West Ham 5 - 2 Burnley Steven Fletcher grabs a goal from inside the six-yard box low into the middle of the goal. West Ham 5-2 Burnley.
73:27 The ball is crossed by Chris Eagles,
71:58 Free kick awarded for a foul by Radoslav Kovac on Steven Fletcher. Chris Eagles restarts play with the free kick.
68:35 Substitution (Burnley) makes a substitution, with Kevin McDonald coming on for Graham Alexander.
68:35 Unfair challenge on Graham Alexander by Zavon Hines results in a free kick. Free kick crossed right-footed by Graham Alexander.
67:06 Chris Eagles provided the assist for the goal.
67:06 GOAL - Steven Fletcher:West Ham 5 - 1 Burnley Steven Fletcher finds the net with a goal from close in to the bottom right corner of the goal. West Ham 5-1 Burnley.
66:35 The official flags Zavon Hines offside. Brian Jensen takes the direct free kick.
64:38 Inswinging corner taken from the left by-line by Chris Eagles, Header by Steven Fletcher from deep inside the penalty area
misses to the left of the target.
63:05 GOAL - Luis Jimenez:West Ham 5 - 0 Burnley Luis Jimenez scores a placed penalty. West Ham 5-0 Burnley.
62:25 Penalty awarded for an unfair challenge on Luis Jimenez by Brian Jensen.
61:24 Andre Bikey challenges Radoslav Kovac unfairly and gives away a free kick. Robert Green takes the direct free kick.
58:24 Substitution Luis Jimenez comes on in place of Guillermo Franco.
57:46 Guillermo Franco concedes a free kick for a foul on Steven Caldwell. Clarke Carlisle takes the direct free kick.
57:02 The ball is swung over by Wade Elliott, Header from close in by David Nugent misses to the right of the target.
56:16 Effort from deep inside the area by David Nugent misses to the right of the target.
55:15 Inswinging corner taken by Junior Stanislas from the left by-line played to the near post, clearance by Andre Bikey.
53:50 Daniel Gabbidon restarts play with the free kick.
53:50 Substitution Christian Kalvenes replaces Stephen Jordan.
53:50 Substitution David Nugent replaces Robbie Blake.
53:50 Free kick awarded for an unfair challenge on Scott Parker by Graham Alexander.
53:01 Steven Caldwell restarts play with the free kick.
53:01 Booking Radoslav Kovac is shown a yellow card for unsporting behaviour.
52:52 Foul by Radoslav Kovac on Andre Bikey, free kick awarded.
52:19 Unfair challenge on Zavon Hines by Stephen Jordan results in a free kick. Radoslav Kovac takes the direct free kick.
50:56 Assist by Junior Stanislas.
50:56 GOAL - Guillermo Franco:West Ham 4 - 0 Burnley Guillermo Franco grabs a headed goal from close range. West Ham 4-0 Burnley.
50:14 Zavon Hines fouled by Stephen Jordan, the ref awards a free kick. Junior Stanislas delivers the ball,
48:34 The referee blows for offside against Zavon Hines. Brian Jensen takes the free kick.
47:48 The assistant referee signals for offside against Steven Fletcher. Robert Green restarts play with the free kick.
47:06 The referee blows for offside. Brian Jensen takes the free kick.
45:01 The second half kicks off.
45:01 Substitution (West Ham) makes a substitution, with Zavon Hines coming on for Carlton Cole.
45:00+3:30 The referee calls an end to the first half.
45:00+0:13 Outswinging corner taken by Robbie Blake from the right by-line.
44:03 Steven Fletcher takes a shot. Daniel Gabbidon gets a block in. Robbie Blake takes a inswinging corner to the near post, clearance
by Daniel Gabbidon.
43:27 Foul by Steven Fletcher on Daniel Gabbidon, free kick awarded. Robert Green restarts play with the free kick.
42:26 Assist by Jonathan Spector.
42:26 GOAL - Carlton Cole:West Ham 3 - 0 Burnley Placed penalty scored by Carlton Cole. West Ham 3-0 Burnley.
41:45 Penalty awarded for an unfair challenge on Jonathan Spector by Robbie Blake.
38:46 Unfair challenge on Graham Alexander by Guillermo Franco results in a free kick. Graham Alexander restarts play with the free
32:57 GOAL - Junior Stanislas:West Ham 2 - 0 Burnley Junior Stanislas scores a goal from close in to the bottom left corner of the goal. West Ham 2-0 Burnley.
32:06 Junior Stanislas takes a shot. Save by Robert Green.
29:26 Graham Alexander gives away a free kick for an unfair challenge on Scott Parker. Free kick crossed left-footed by Herita Ilunga
from left wing, Andre Bikey makes a clearance.
28:42 Scott Parker takes a shot from just outside the penalty area clears the crossbar.
27:39 The referee blows for offside against Carlton Cole. Brian Jensen takes the direct free kick.
25:43 The assistant referee signals for offside against Guillermo Franco. Clarke Carlisle takes the direct free kick.
24:50 Free kick awarded for an unfair challenge on Daniel Gabbidon by Andre Bikey. Robert Green takes the free kick.
24:10 The ball is delivered by Herita Ilunga, Guillermo Franco produces a header from inside the area that goes over the bar.
21:50 Effort on goal by Wade Elliott from just inside the area clears the bar.
21:16 Daniel Gabbidon gives away a free kick for an unfair challenge on Steven Fletcher. Direct free kick taken by Graham Alexander.
18:55 Free kick awarded for a foul by Steven Fletcher on Herita Ilunga. Free kick taken by Robert Green.
17:05 Assist by Scott Parker.
17:05 GOAL - Jack Collison:West Ham 1 - 0 Burnley Jack Collison finds the back of the net with a goal from inside the penalty area to the bottom right corner of the goal. West
Ham 1-0 Burnley.
16:21 Wade Elliott concedes a free kick for a foul on Scott Parker. Free kick taken by Scott Parker.
14:19 Robbie Blake takes the inswinging corner, clearance made by Scott Parker.
13:46 Foul by Jack Collison on Stephen Jordan, free kick awarded. Free kick taken by Brian Jensen.
12:14 Unfair challenge on Radoslav Kovac by Steven Fletcher results in a free kick. Direct free kick taken by Scott Parker.
11:15 Jack Collison sends in a cross, Guillermo Franco takes a shot.
8:25 Outswinging corner taken right-footed by Robbie Blake from the right by-line, Clarke Carlisle takes a shot. Blocked by Scott
7:55 The ball is crossed by Chris Eagles.
4:56 Andre Bikey takes a shot. Save by Robert Green. Andre Bikey takes a shot. Jonathan Spector gets a block in. Robbie Blake takes
a inswinging corner to the near post, clearance made by Carlton Cole.
1:58 The assistant referee flags for offside against Chris Eagles. Robert Green restarts play with the free kick.
1:09 Chris Eagles challenges Scott Parker unfairly and gives away a free kick. Scott Parker restarts play with the free kick.
0:00 The referee gets the game started.
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