Neil Warnock, with one eye on a crucial clash with Chelsea on Saturday, made 11 changes from the side that lost 2-0 at Everton last weekend.
Former Blues keeper Ian Bennett was kept busy early on keeping out a Neil Danns effort before diving to his left to palm away Stephen Kelly's stinging shot from 15 yards.
United swept ahead in the 21st minute with a goal worthy of the Premiership.
Danny Webber, given too much space on the right flank, threaded the ball to Ade Akinbiyi, who looped it into the far corner with the most delicate of touches.
Cameron Jerome, a target for Warnock last season, almost snatched an equaliser with a stinging shot which was blocked by Bennett before United squandered a chance to grab a second.
Akinbiyi picked out Paul Ifill who cut inside, but with the unmarked Steven Kabba screaming for the ball, Ifill swivelled and shot wide of the far post.
Bennett produced another crucial save to keep out DJ Campbell before Birmingham were back on level terms in the 41st minute with a freak goal.
United captain Chris Morgan tried to pass back to his keeper but the ball cannoned off Campbell's shins and looped into the net from 15 yards with Bennett stranded.
Dangerman Campbell was stopped by the woodwork in the 54th minute after getting the better of veteran defender Craig Short, but again he could find no way past Bennett as the keeper stuck out a hand to deflect the ball against the foot of the post.
Substitute Nicklas Bendtner struck in the 71st minute as, after Martin Taylor headed the ball forward, Bendtner raced 30 yards to skip around the stranded Bennett and slot into an empty net.
Jerome latched on to a miscued Short back pass to sidestep Bennett for Birmingham's third in the 78th minute, before midfielder Nick Montgomery scored with a scorching shot from 25 yards with five minutes to go.
However, Sebastian Larsson had the last word deep into injury time slotting home substitute Neil Kilkenny's cross.