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.