The travelling fans were on their feet when he was brought down on the edge of the box by Maynor Figueroa, but the referee waved away the shouts for a penalty.
Koumas was a constant threat on the left for Wigan, but it was Jordi Gomez who went closest to giving them the lead when he drew a full-stretch save from Green after a neat exchange of passes with Rodallega.
Martinez pleased with 'complete performance'
Hines was involved again as he nearly made Kirkland pay for taking his time over dealing with a Titus Bramble back pass when he appeared from nowhere to give the former England keeper a scare.
Green, England's current number one, was then tested from distance by both Gomez and Rodallega just before the end of a forgettable first half, which ended with Hammers striker Carlton Cole putting the ball in the net only to find the whistle had already gone.
The match desperately needed a goal, and it duly came 10 minutes after the restart.
Rodallega was quickest to react when Green blocked Koumas's close-range shot, and the goal seemed to inject some much-needed urgency into the match.
Zola wants Hammers improvement
West Ham substitute Diamanti almost had a dramatic impact shortly after he came on for Radoslav Kovac, rattling the far post from a tight angle.
But the visitors' lack of punch in front of goal suggested an equaliser was never likely, with Wigan always looking a better bet to add a second.
Wigan manager Roberto Martinez:
"The way the players adapted to what was needed was exceptional, we had to stop West Ham playing their football which was a big test, so a clean sheet and three points is what we deserved.
"We're still growing, in a phase when were need to look behind the results and make sure we grow together. You can see the winning mentality in the dressing room - we want to be as good as we can and that will take time.
"Overall it was a very complete performance, it's another step forward."
West Ham manager Gianfranco Zola:
"In the first half I thought we controlled the game well and we looked better than them.
"The goal was sloppy, we didn't start the second half in the same frame of mind that we did the first - that's something we need to work on.
"Alessandro Diamanti is a player who has got a lot of quality, now he needs to get use to the pace of the Premier League - I'm sure he will have a big impact on the game."
90:00+5:44 The final whistle goes and the game is over.
90:00+5:07 Charles N'Zogbia challenges Valon Behrami unfairly and gives away a free kick. Julien Faubert takes the free kick.
90:00+4:42 Free kick awarded for an unfair challenge on Scott Parker by Scott Sinclair. Direct free kick taken by Robert Green.
90:00+4:18 Charles N'Zogbia takes a short corner.
90:00+3:02 The ball is crossed by James Tomkins, clearance made by Maynor Figueroa.
90:00+2:36 The referee penalises Maynor Figueroa for handball. Indirect free kick taken by Robert Green.
90:00+1:13 Titus Bramble takes the free kick.
90:00+1:13 Substitution Scott Sinclair comes on in place of Jordi Gomez.
90:00+1:13 Jordi Gomez fouled by Frank Nouble, the ref awards a free kick.
90:00+0:36 Jordi Gomez gives away a free kick for an unfair challenge on Daniel Gabbidon. Alessandro Diamanti takes the free kick.
88:57 The assistant referee flags for offside against Charles N'Zogbia. Robert Green takes the free kick.
88:13 Short corner taken by Charles N'Zogbia from the left by-line.
87:38 Matthew Upson concedes a free kick for a foul on Jordi Gomez. Free kick taken by Jordi Gomez.
87:01 Handball by Carlton Cole. Indirect free kick taken by Chris Kirkland.
86:40 Daniel Gabbidon concedes a free kick for a foul on Mohamed Diame. Jordi Gomez restarts play with the free kick.
85:35 Substitution Mark Noble leaves the field to be replaced by Frank Nouble.
85:35 The ball is sent over by Alessandro Diamanti, Scott Parker has a headed effort at goal from deep inside the area missing to
the right of the target.
83:33 Effort from the edge of the area by Jordi Gomez goes wide of the right-hand post.
82:27 Free kick taken by Alessandro Diamanti.
82:27 Booking Titus Bramble is cautioned by the ref for unsporting behaviour.
82:21 Free kick awarded for an unfair challenge on Zavon Hines by Titus Bramble.
78:53 Short corner worked by Alessandro Diamanti.
78:04 Alessandro Diamanti produces a left-footed shot from outside the area and hits the bar.
76:33 Outswinging corner taken from the left by-line by Charles N'Zogbia, Headed effort from inside the area by Maynor Figueroa
misses to the left of the goal.
74:53 Hendry Thomas has an effort at goal from outside the area missing to the wide right of the goal.
73:54 Jordi Gomez takes a shot. Robert Green makes a save.
71:45 Substitution Jason Scotland on for Hugo Rodallega.
68:03 Direct strike on goal from the free kick comes in from Alessandro Diamanti.
68:03 Booking Maynor Figueroa is given a yellow card.
67:49 Maynor Figueroa challenges Zavon Hines unfairly and gives away a free kick.
66:50 Free kick awarded for an unfair challenge on Hendry Thomas by Carlton Cole. Titus Bramble takes the free kick.
64:14 Substitution Jason Koumas goes off and Paul Scharner comes on.
64:14 Effort from deep inside the area by Zavon Hines misses to the right of the goal.
63:46 Jordi Gomez has an effort from just inside the box that misses to the left of the target.
63:14 Free kick awarded for an unfair challenge on Hendry Thomas by Valon Behrami. Free kick taken by Hendry Thomas.
62:06 Substitution Junior Stanislas goes off and Alessandro Diamanti comes on.
62:06 Substitution Valon Behrami replaces Radoslav Kovac.
61:01 Outswinging corner taken by Mark Noble, assist on the goal came from Jason Koumas. Clearance by Maynor Figueroa.
58:55 Mark Noble takes the outswinging corner, Scott Parker takes a shot. Save made by Chris Kirkland. Inswinging corner taken right-footed
by Mark Noble from the left by-line, Headed effort from deep inside the area by James Tomkins misses to the right of the goal.
57:17 Corner taken by Mark Noble, James Tomkins has a headed effort at goal from deep inside the area missing to the right of the
54:56 GOAL - Hugo Rodallega:Wigan 1 - 0 West Ham Hugo Rodallega grabs a goal from close range low into the middle of the goal. Wigan 1-0 West Ham.
54:49 Jason Koumas takes a shot. Save by Robert Green.
54:29 Charles N'Zogbia sends in a cross, clearance by Matthew Upson.
49:09 Unfair challenge on Mark Noble by Hugo Rodallega results in a free kick. James Tomkins takes the free kick.
48:08 Maynor Figueroa concedes a free kick for a foul on Zavon Hines. Mark Noble crosses the ball from the free kick right-footed
from right wing.
47:13 Corner taken by Charles N'Zogbia from the right by-line to the near post, Carlton Cole manages to make a clearance.
45:01 The second half kicks off.
45:00+1:29 The referee blows for half time.
45:00+0:51 Hendry Thomas challenges Scott Parker unfairly and gives away a free kick. Scott Parker takes the direct free kick.
42:37 Corner taken by Mark Noble played to the near post.
41:28 Jordi Gomez takes a shot. Save by Robert Green. Short corner worked by Jason Koumas. The ball is crossed by Jason Koumas,
James Tomkins makes a clearance.
40:41 Carlton Cole is ruled offside. Titus Bramble restarts play with the free kick.
39:21 Hugo Rodallega takes a shot. Save by Robert Green. Corner crossed in by Jordi Gomez.
36:53 Jason Koumas sends in a cross.
33:59 Carlton Cole gives away a free kick for an unfair challenge on Emmerson Boyce. Free kick taken by Chris Kirkland.
33:21 Mario Melchiot takes a shot. Blocked by Scott Parker.
32:09 The referee blows for offside. Direct free kick taken by Titus Bramble.
31:40 Zavon Hines takes a shot. Save made by Chris Kirkland.
29:11 A cross is delivered by Maynor Figueroa, clearance made by Matthew Upson.
27:19 Free kick taken by Maynor Figueroa.
27:19 Booking Mark Noble is booked.
27:13 Mark Noble challenges Hendry Thomas unfairly and gives away a free kick.
25:17 Free kick awarded for an unfair challenge on Zavon Hines by Hendry Thomas. Mark Noble restarts play with the free kick. Junior
Stanislas takes a shot. Save by Chris Kirkland. Mark Noble takes a outswinging corner from the right by-line played to the
near post, Carlton Cole takes a shot. Chris Kirkland makes a save.
23:27 Scott Parker concedes a free kick for a foul on Hendry Thomas. The free kick is swung in left-footed by Jordi Gomez, clearance
by Matthew Upson.
22:41 The referee blows for offside against Carlton Cole. Chris Kirkland takes the free kick.
22:16 Mohamed Diame concedes a free kick for a foul on Matthew Upson. Direct free kick taken by Scott Parker.
20:53 Free kick awarded for a foul by Hendry Thomas on Carlton Cole. Scott Parker restarts play with the free kick.
19:54 A cross is delivered by Jason Koumas, clearance made by James Tomkins.
19:30 Emmerson Boyce fouled by Zavon Hines, the ref awards a free kick. Emmerson Boyce takes the direct free kick.
17:14 James Tomkins fouled by Hugo Rodallega, the ref awards a free kick. Free kick taken by Scott Parker.
17:00 Carlton Cole takes a shot. Save by Chris Kirkland.
15:54 Free kick awarded for a foul by Carlton Cole on Mario Melchiot. The free kick is delivered left-footed by Charles N'Zogbia
from right wing.
12:18 Right-footed shot by Mohamed Diame went wide left of the goal.
9:34 Jordi Gomez takes a shot. Save by Robert Green.
8:20 The offside flag is raised against Zavon Hines. Indirect free kick taken by Emmerson Boyce.
7:40 Zavon Hines is caught offside. Chris Kirkland takes the indirect free kick.
6:28 Free kick awarded for a foul by Titus Bramble on Zavon Hines. Junior Stanislas has an effort direct from the free kick.
1:41 Zavon Hines gives away a free kick for an unfair challenge on Emmerson Boyce. Free kick taken by Emmerson Boyce.
0:00 The ref blows the whistle to begin the match.
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