Blues manager Steve Bruce said: "It was a good match to win after some anxious early moments."
Leeds boss Eddie Gray was disappointed, commenting: "We tested Birmingham for long spells and had a lot of attacking play but we could not take our chances."
The Whites are still fighting for their lives and there was plenty of encouraging play from Mark Viduka but the failure of the Australian to capitalise upon some good opportunities cost the Yorkshire club the match.
Last time out a shocking performance from The Blues backline saw them crash 5-3 at Middlesbrough and it seemed they had not learned their lessons.
United's intent was clear as early as the first minute when Viduka saw a close-range shot pushed around the post by Maik Taylor following a smart pass from Alan Smith.
But the Australian striker made no mistake in the third minute. Jermaine Pennant slipped a throughball down the channel and, with Matt Upson unable to cut off the pass, Viduka powered his way through the middle and slipped a low shot under Taylor to break the deadlock.
Birmingham had to chase the game, but it only exposed their brittle rearguard and they were fortunate not to fall further behind when James Milner crossed from the right and, with the goal at his mercy, Viduka conspired to shoot into the side netting. A contender for miss of the season.
It was an expensive miss as Birmingham were able to get back on level terms in the 12th minute, when Stan Lazaridis flicked on Clinton Morrison's cross for the unmarked Bryan Hughes to score.
Following the hectic start the game settled down, with City emerging as the more dangerous side, Didier Domi was forced into a goal line clearance from Forssell and Martin Grainger struck the crossbar.
Leeds looked the better side at the start of the second half and there were no signs of the collapse that was in store. Viduka headed tamely, Milner saw one shot saved after a decent run and volleyed another shot wide.
Kenny Cunningham's 30-yard back-pass then took an horrendous bobble over Maik Taylor's foot but ended up rolling wide.
With Viduka firing on all cylinders Leeds were always a danger, but in the 67th minute Lazaridis set up an easy goal for Hughes and this signalled a collapse by the visitors.
Two minutes later a throughball from Kenny Cunningham was collected on the run by Forssell to notch his 17th goal of the season, despite offside protests from Leeds.
Forssell then converted an 80th minute penalty after Steve Caldwell was adjudged to have fouled Clinton Morrison to complete the rout.
Man of the Match: Stan Lazaridis
The Australian winger set up two and was a constant threat to Leeds' struggling backline.