Manchester United reached the Carling Cup semi-finals thanks to a devastating 18-minute second half attacking spell.
Within 60 seconds of the restart Louis Saha had the simplest of tasks in tapping in Cristiano Ronaldo's cross.
United extended their lead in the 50th minute when Park Ji-Sung lashed the ball into the net with a powerful shot.
Saha claimed his second goal - the best of United's three strikes - when he guided a shot past Maik Taylor, before Jiri Jarosik headed in for the Blues.
Second from bottom in the Premiership, Birmingham have developed an alarming habit of conceding goals in quick bursts.
On Saturday they had left their manager Steve Bruce fuming after they let in three goals in the space of 40 minutes in their 4-1 defeat at Manchester City on Saturday.
Birmingham matched United for the first half, but once Saha put the visitors ahead there was only going to be one winner.
The worry for Bruce is that Birmingham's defence looks so shaky and they made another uncertain start, with Kieran Richardson's cross causing them problems in the opening minute.
The 18-year-old Guiseppe Rossi gave Birmingham an even bigger fright in the third minute, volleying the ball against the bar following Gary Neville's free-kick.
On 20 minutes Rossi's striking partner Saha nipped in front of Damien Johnson only to steer his header wide of the post from a promising position.
In contrast to United's rapier-like attacks, Birmingham's build-up play was more considered as they looked to use Heskey's strength to hold up the ball.
Having previously gone close with a header from a free-kick, Heskey shook off the attentions of Wes Brown to strike a fierce shot that Tim Howard did well to turn round the post.
United manager Sir Alex Ferguson opted to withdraw Rossi at the break, introducing Wayne Rooney for the Italian.
Given how well Rooney has played this season, the irony was that he played absolutely no part in those three second-half goals, apart that is to congratulate his teammates.
Ronaldo's sprint down the right wing left Marcos Painter trailing in his wake and the Portuguese winger's cross was expertly converted by Saha.
Five minutes later Birmingham laboured to clear the ball and Park crashed a shot past Taylor as he scored his first goal in United colours.
United's third goal owed much to Neville's energy and vision, the United right-back picking out Saha after an intelligent run.
Running across the edge of the Birmingham area, Saha worked himself a modicum of space before curling the ball into the roof of the net.
With a quarter of an hour to go Jarosik headed in a Jermaine Pennant free-kick to give the home crowd something to cheer about as a miserable 2005 draws to a close for them.
Birmingham manager Steve Bruce:
"It's going to be a tough winter but I'm confident we can pull through.
"The way we finished the first-half, to start the second-half like that was a great disappointment.
"Two goals in four minutes has killed us with that little bit of quality."
Manchester United manager Sir Alex Ferguson:
"Park Ji-Sung has been so close in so many games this season - it was a great goal as well.
"When you are in the semi-final of any cup you must go for it. We'll certainly give it a good shot this year.
"Last year I thought we were very unlucky against Chelsea in the semis."
Birmingham: Maik Taylor, Johnson, Martin Taylor, Upson, Painter, Pennant, Butt (Clapham 67), Clemence, Dunn (Kilkenny 66), Heskey (Forssell 82), Jarosik.
Subs Not Used: Doyle, Pandiani.
Goals: Jarosik 75.
Man Utd: Howard, Neville, Brown, Silvestre (Ferdinand 60), Richardson, Ronaldo, O'Shea (Jones 66), Fletcher, Park, Rossi (Rooney 45), Saha.
Subs Not Used: Van der Sar, Bardsley.
Booked: Silvestre, Richardson.
Goals: Saha 46, Park 50, Saha 63.
Ref: M Halsey (Lancashire).