Hayden Mullins’ 71st-minute goal condemned United to another poor result away from home and inflicted a first loss on new Leeds manager Brian McDermott at St Andrews.
Results elsewhere ruled his side out of the intense battles at either end of the division.
Leeds side rode their luck before the break, relying on the woodwork to maintain parity, but they were first to threaten after the interval when Ross McCormack’s ambitious free-kick beat Jack Butlands’ fingertips and clipped the top of the crossbar.
The Scotland international saw another effort fly wide soon after, deflecting off a defender after Stephen Warnock picked him out inside Birmingham’s box, and a third chance went begging when McCormack teed up a cross and volleyed it beyond Butland’s left-hand post.
Birmingham struggled to maintain their impetus going forward and a Nikola Zigic volley was a rare effort on Paddy Kenny’s goal. Sam Byram went closer when Butland’s error gave him a difficult opportunity which the defender hooked into the side-netting.
But City produced the opening goal from very little as Kenny parried a Nathan Redmond strike into the path of Mullins an invited the midfielder to tap home the loose ball from close range.
Butland protected Birmingham’s lead with a good save from Rodolph Austin on 75 minutes and United did not trouble the keeper again.
Despite the defeat, McDermott is still feeling optimistic about the future at Elland Road.
He said: “I thought we should have got something out of the game. When it was 0-0 we were on top and then they scored from nothing.
“When I arrived at the club I put my reputation on the line and to make sure Leeds remained in this division. So far as I am concerned it is job done.
“Everyone must be going in the same direction. If that occurs in this club you have a major chance.
“I think we have to talk about who needs to come in. If we can add to the squad with good quality players who know this division we should progress.
“Leeds were possibly in trouble when I came in. I am delighted with the boys. They played two games at home and we won them both. They were pressure games.”