Substitute Kieran Lee struck with two minutes of extra time remaining to send holders Manchester United into the fourth round of the Carling Cup.
Lee's assured finish secured a dramatic win for Man Utd
A vibrant Crewe side had looked the more likely winners before debutant Lee slid home Alan Smith's through-ball.
United had gone ahead through Ole Gunnar Solskjaer's 26th-minute strike.
But the hosts deservedly equalised when the lively Luke Varney cut inside and beat Tomasz Kuszczak with a low shot, sending the tie into extra time.
It was cruel luck for Dario Gradi's side, who were more than a match for a youthful United.
Smith made his first start since February for the visitors but he and strike partner Phil Marsh saw little of the ball in the opening period of the game.
Instead it was Kuszczak who shone for United as he prevented Crewe taking the lead by somehow stopping Neil Cox's header from Ben Rix's clever free-kick.
The Polish keeper was then at full stretch to deny Isaac Osbourne and though Varney stabbed home the rebound, the linesman raised his flag for offside.
But against the run of play, Solskjaer celebrated his first Carling Cup appearance since 2003 with a beautifully-taken goal.
Crewe keeper Ben Williams then kept the half-time score at 1-0 with a fingertip save from Kieran Richardson's volley.
The game settled into a more pedestrian pace at the start of the second half but it sprang back to life when Varney let fly from 20 yards.
They could even have won it in normal time, but Kuszczak was equal to Varney's fierce shot.
Richardson should have sealed the tie eight minutes from time when he was sent clean through by Solskjaer but, after steadying himself, he fired his shot against the post.
In extra time, Jon Otsemobor came close to clinching a famous win for his side but Kuszczak turned away his angled shot and just as penalties loomed, Lee made a name for himself with an assured finish.
Crewe boss Dario Gradi:
"I feel satisfied. I asked for a memorable game and I got it, there is no doubt about that.
"Probably that bit better quality meant they scored and we didn't but in terms of creating chances we probably created more and given as good as we've got."
Manchester United boss Sir Alex Ferguson:
"We were a bit lucky because I think Crewe were the better team.
"It's an amazing game because we had a team with seven internationals out there and you would expect them to win.
"But you have to work hard before you have the right to win a game and our players didn't do that."
Crewe: Williams, Otsemobor, Baudet (O'Donnell 110), Cox, Taylor (Bell 76), Lowe, Rix, Osbourne, Vaughan, Varney, Maynard.
Subs Not Used: Tomlinson, Rodgers, Higdon.
Goals: Varney 73.
Man Utd: Kuszczak, Gray (Lee 77), Brown, Silvestre, Heinze, Marsh (Barnes 46), David Jones, Ritchie Jones, Richardson, Smith, Solskjaer, Barnes (Shawcross 103).
Subs Not Used: Heaton, Rose.
Booked: Richardson, Lee, Brown.
Goals: Solskjaer 26, Lee 119.
Ref: C Foy (Merseyside).