Javier Hernandez came off the bench to score a last-minute winner as holders Manchester United earned a Carling Cup quarter-final place at Wolves' expense.
Hernandez had only been on for eight minutes when he settled a thrilling tie by firing in off Wayne Hennessey.
Bebe had put United ahead on his first start with a deflected strike before George Elokobi headed in to equalise.
Park Ji-Sung lashed home to make it 2-1 but Kevin Foley's turn and low finish levelled again before Hernandez won it.
It was an exciting climax to the game but perhaps harsh on the visitors, who more than played their part in a second half of wonderful end-to-end football.
Yet it had all started so differently, with a first 45 minutes none of the 46,083 present will be in a hurry to remember.
As is their wont in the Carling Cup, both managers made changes to their line-ups, with United replacing their entire starting XI and Wolves bringing in seven new players.
It was immediately obvious that the players were not comfortable in each other's company as the first period passed by in a blur of misplaced passes, with wastefulness in possession a recurring theme.
Bebe was the best of the United bunch, the £7.4m summer signing trying to rid the game of its lethargy by testing Elokobi down the United right, one cross finding Federico Macheda only for the Italian to shoot tamely at Hennessey.
Wolves were similarly sluggish, with only Foley and Matt Jarvis down their right providing any sort of threat, but the half-time whistle was the best thing that could happen to the game.
It was a completely different contest after the break as both teams began playing with an urgency that had been badly lacking, chances soon coming thick and fast at either end.
United were the first to pour forward as Macheda curled over and then Park fired at the legs of Hennessey, but they went ahead when Bebe's shot from an angle on the right deflected cruelly off Elokobi and looped over Hennessey, with Foley narrowly failing to head the ball off the line.
Wolves had not scored at Old Trafford since February 1980 but they were not to be denied this time, and after Fabio brilliantly deflected Stephen Hunt's goalbound drive over the bar, the visitors equalised when Elokobi nodded in the resulting corner.
Foley squeezes his shot in to get Wolves level at 2-2
It was the full-back's first goal for the club and Wolves were suddenly flying, Hunt clipping the top of the bar with his left-foot shot after a run and cross down the left from the excellent Jarvis.
The game had opened up to a dramatic degree, so it was no real surprise when the teams exchanged goals once more, both efforts superbly crafted.
United went ahead again when Park burst forward from midfield and after an unwitting touch from Steven Mouyokolo, the South Korean slammed into the corner, before Steven Fletcher's cheeky flick teed up Foley to shoot low beyond United keeper Ben Amos, making only his second start for the club.
Wolves went perilously close to taking the lead when Sylvan Ebanks-Blake saw his ferocious left-foot drive from 18 yards fly only inches past Amos's right-hand post, but it was United's new hero Hernandez who once again had the last word.
Fresh from his two-goal match-winning display in the Premier League at Stoke on Sunday, Hernandez collected Darron Gibson's pass and fired in via Hennessey's body to win it in the dying stages.
90:00+5:36 The final whistle goes and the game is over.
90:00+4:02 Marcus Bent is ruled offside. Ben Amos takes the indirect free kick.
90:00+4:02 Substitution Ji-Sung Park leaves the field to be replaced by Ravel Morrison.
90:00+2:29 Kevin Foley produces a left-footed shot from long range that goes harmlessly over the bar.
89:24 Assist by Darron Gibson.
89:24 GOAL - Javier Hernandez:Man Utd 3 - 2 Wolverhampton Javier Hernandez fires in a goal from inside the box to the bottom left corner of the goal. Man Utd 3-2 Wolverhampton.
84:40 Substitution Kevin Doyle on for Matthew Jarvis.
84:30 Effort from the edge of the area by Gabriel Obertan goes wide of the right-hand upright.
83:50 Federico Macheda is flagged offside by the assistant referee. Free kick taken by Kevin Foley.
82:59 Gabriel Obertan takes a shot. Save made by Wayne Hennessey.
81:58 Marcus Bent takes a shot. Ben Amos makes a save.
79:54 Substitution (Man Utd) makes a substitution, with Javier Hernandez coming on for Tiago Bebe.
79:54 Substitution Marcus Bent joins the action as a substitute, replacing Sylvan Ebanks-Blake.
79:15 Short corner worked by Matthew Jarvis.
78:29 The official flags Federico Macheda offside. Wayne Hennessey takes the free kick.
77:49 Sylvan Ebanks-Blake produces a left-footed shot from the edge of the area and misses to the left of the goal.
75:42 Assist on the goal came from Steven Fletcher.
75:42 GOAL - Kevin Foley:Man Utd 2 - 2 Wolverhampton Kevin Foley finds the back of the net with a goal from inside the penalty box low into the middle of the goal. Man Utd 2-2
74:43 David Jones has shot on goal from just outside the box which goes wide of the right-hand upright.
73:23 Substitution Fabio Da Silva goes off and Gary Neville comes on.
71:32 Darron Gibson takes a shot. Save made by Wayne Hennessey.
69:50 GOAL - Ji-Sung Park:Man Utd 2 - 1 Wolverhampton Ji-Sung Park finds the back of the net with a goal from inside the area to the top right corner of the goal. Man Utd 2-1 Wolverhampton.
69:26 Steven Fletcher is caught offside. Michael Carrick restarts play with the free kick.
67:26 Steven Fletcher produces a left-footed shot from just outside the area that goes harmlessly over the bar.
66:43 Darron Gibson challenges Michael Mancienne unfairly and gives away a free kick. Direct free kick taken by Kevin Foley.
66:43 Booking The referee cautions Darron Gibson for unsporting behaviour.
65:00 The ball is delivered by Tiago Bebe, Close range shot by Federico Macheda goes over the bar.
63:51 Steven Fletcher takes a shot and went wide left of the target.
62:56 Ji-Sung Park produces a right-footed shot from just outside the box that goes wide left of the target.
62:12 Stephen Hunt takes a shot.
59:24 Corner taken by David Jones, assist on the goal came from David Jones.
59:24 GOAL - George Elokobi:Man Utd 1 - 1 Wolverhampton George Elokobi fires in a goal from close range low into the middle of the goal. Man Utd 1-1 Wolverhampton.
58:55 Stephen Hunt takes a shot. Blocked by Fabio Da Silva.
58:05 Centre by Matthew Jarvis.
55:25 Assist on the goal came from Gabriel Obertan.
55:25 GOAL - Tiago Bebe:Man Utd 1 - 0 Wolverhampton Tiago Bebe finds the back of the net with a goal from deep inside the penalty box high into the middle of the goal. Man Utd
55:03 Sylvan Ebanks-Blake takes a shot. Chris Smalling gets a block in.
54:23 Darron Gibson takes the inswinging corner, save made by Wayne Hennessey.
54:09 Ji-Sung Park takes a shot. Save made by Wayne Hennessey.
52:16 Unfair challenge on Tiago Bebe by Michael Mancienne results in a free kick. Direct effort from the free kick comes in from
Darron Gibson, save made by Wayne Hennessey.
51:29 Federico Macheda produces a right-footed shot from inside the area that clears the bar.
50:15 Christophe Berra fouled by Federico Macheda, the ref awards a free kick. Direct free kick taken by Christophe Berra.
49:38 Stephen Hunt delivers the ball.
48:27 Matthew Jarvis sends in a cross, Effort from deep inside the area by Steven Fletcher misses to the left of the target.
46:43 Michael Carrick produces a right-footed shot from just outside the area that goes harmlessly over the target.
45:01 The second half has started.
45:00+1:04 The first half comes to an end.
44:58 Tiago Bebe takes a shot from just outside the penalty area clears the crossbar.
43:57 Foul by Stephen Hunt on Fabio Da Silva, free kick awarded. Ben Amos takes the direct free kick.
43:15 Free kick awarded for a foul by Tiago Bebe on George Elokobi. Direct free kick taken by Wayne Hennessey.
41:22 Free kick awarded for an unfair challenge on Sylvan Ebanks-Blake by Chris Smalling. Matthew Jarvis crosses the ball from the
free kick right-footed from left wing, save by Ben Amos.
39:57 Matthew Jarvis challenges Tiago Bebe unfairly and gives away a free kick. Direct free kick taken by Tiago Bebe.
39:42 Matthew Jarvis takes a shot. Blocked by Chris Smalling.
39:28 Kevin Foley delivers the ball, Wes Brown manages to make a clearance.
39:13 Short corner worked by David Jones.
36:53 Foul by Jonathan Evans on Sylvan Ebanks-Blake, free kick awarded. David Jones takes the free kick.
34:21 Free kick awarded for a foul by Jonathan Evans on Steven Fletcher. Direct strike on goal from the free kick comes in from
33:09 Federico Macheda concedes a free kick for a foul on Christophe Berra. Free kick taken by Christophe Berra.
31:21 Inswinging corner taken left-footed by David Jones, save by Ben Amos.
30:38 Effort by Michael Carrick from a long way out goes over the crossbar.
29:55 Steven Fletcher is ruled offside. Chris Smalling takes the indirect free kick.
27:50 Tiago Bebe concedes a free kick for a foul on George Elokobi. Wayne Hennessey takes the direct free kick.
27:05 The official flags Federico Macheda offside. Free kick taken by Kevin Foley.
26:07 Outswinging corner taken by Darron Gibson from the right by-line.
25:55 Centre by Tiago Bebe, Christophe Berra makes a clearance.
22:38 The ball is swung over by Kevin Foley, Wes Brown makes a clearance. Inswinging corner taken right-footed by Matthew Jarvis
from the left by-line to the near post, Steven Mouyokolo has a header from close range and clears the crossbar.
22:24 Foul by Fabio Da Silva on Stephen Hunt, free kick awarded. David Jones takes the free kick.
21:01 Tiago Bebe fouled by Sylvan Ebanks-Blake, the ref awards a free kick. Free kick taken by Wes Brown.
19:37 Foul by Sylvan Ebanks-Blake on Chris Smalling, free kick awarded. Chris Smalling takes the free kick.
18:41 Federico Macheda takes a shot. Wayne Hennessey makes a save.
15:46 Unfair challenge on Steven Fletcher by Wes Brown results in a free kick. Stephen Hunt produces a cross, Header from deep inside
the area by Sylvan Ebanks-Blake goes harmlessly over the crossbar.
13:00 The assistant referee signals for offside against Ji-Sung Park. Wayne Hennessey takes the indirect free kick.
12:40 The official flags Federico Macheda offside. Christophe Berra takes the free kick.
12:03 Darron Gibson concedes a free kick for a foul on Sylvan Ebanks-Blake. Direct free kick taken by David Jones.
11:37 Gabriel Obertan takes a shot. Wayne Hennessey makes a save.
11:31 Fabio Da Silva produces a cross, Steven Mouyokolo manages to make a clearance.
10:54 Free kick awarded for an unfair challenge on Chris Smalling by Matthew Jarvis. Ben Amos takes the direct free kick.
10:17 Free kick awarded for a foul by Jonathan Evans on Sylvan Ebanks-Blake. Direct free kick taken by Kevin Foley.
7:27 Inswinging corner taken by Darron Gibson, save by Wayne Hennessey.
6:35 Darron Gibson decides to take a short corner.
6:17 Darron Gibson takes a shot. Michael Mancienne gets a block in.
4:24 Inswinging corner taken by David Jones from the right by-line.
0:00 The game begins.
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