Gallant Wrexham had taken Birmingham into extra-time when the Welsh club began to flag badly under increasing pressure engineered by substitute David Dunn.
Dunn produced the third goal with fellow substitute Nicklas Bendtner running in a fourth goal in the 117th minute which was hardly a reflection of overall tie.
The surprising feature of the game was that struggling Wrexham were able to take the game into extra-time before they surrendered three goals.
Birmingham made eight changes from the side which played Ipswich as manager Steve Bruce gave his second choice players an opportunity to prove themselves.
Despite facing opposition which had conceded ten goals in their previous two games, Birmingham struggled to apply attacking pressure and there was a definite lack of thrust in their play as they were surprisingly thwarted without any difficulty.
Wrexham were more positive in their approach play and were prepared to take the game to Birmingham which often proved to be more than a little embarrassing for the Championship joint-leaders.
Often it was Josh Johnson, a young lad from Trinidad making his first appearance for the Welsh club, who proved to be a lively character and regularly posed problems for Stephen Kelly.
Surprisingly he operated on the left but often had to cut back to cross with his right foot which enabled Birmingham on a couple of occasions to re-group to avoid trouble.
Cameron Jerome wasted a good opportunity to put Birmingham ahead but produced a weak finish and later a McSheffrey free-kick bounced off the former Cardiff player and the ball went wide.
From this let-off Wrexham stormed into a shock lead in the 29th minute after Colin Doyle had made a tremendous save to keep out a left-footed rocket from John McAliskey.
Skipper Darren Ferguson took the left-wing corner and it was headed on by Mike Williams to Chris Llewellyn who turned to fire past Doyle.
Jerome finally made amends four minutes before the break when the young striker bundled home a left-wing cross from McSheffrey.
A minute later Mikael Forssell lashed his shot wide with only goalkeeper Michael Ingham to beat and the wasted opportunity undoubtedly kept Wrexham in the game.
A double substitution by Birmingham with Bendtner and DJ Campbell replacing Forssell and Jerome appeared to have done the trick when Ingham brought down Campbell.
But the former Brentford striker agonisingly screwed his 67th minute spot-kick wide of the post to the continued frustration of the Birmingham fans.
McSheffrey hit the bar with a free-kick in the first period of extra time and in the 102nd minute his powerful shooting earned him Birmingham's second goal with a 25 yard pile-driver.
Dunn capped a good final 30 minutes when he scored on the a break in the 113th minute following a pass from Neil Kilkenny and Bendtner set the seal on the victory soon after.