Town returned to the top six with a deserved win at Elland Road thanks to Tommy Smith’s first-half header.
Blues carved out a number of chances, with Daryl Murphy and Ryan Fraser both going close, while Dean Gerken had hardly a save to make at the other end.
The winner came just past the half hour, Smith heading in his second goal of the season to end Leeds’ unbeaten record this term and return Blues to winning ways.
Town made two changes to the side that went down at Reading on Friday, Ainsley Maitland-Niles and Daryl Murphy in for Brett Pitman and the injured Freddie Sears.
Sol Bamba picked up a yellow card inside the first seven minutes when he took out Ryan Fraser down the left flank, David McGoldrick seeing his shot blocked from the free-kick.
Luke Chambers did superbly to rob Lewis Cook as he burst into the box from Chris Wood’s pass, then Maitland-Niles was crowded out inside the Leeds’ penalty area in an even opening to the game.
Marco Silvestri held firm from Chambers’ free-kick as Murphy challenged, then Mirco Antenucci had his shot deflected into Dean Gerken’s hands by Christophe Berra’s block.
Gaetano Berardi fired wide from distance as the half hour mark was reached without either ‘keeper really being tested but on 31 minutes, Blues were in front, Silvestri misjudging the corner, Leeds didn’t deal with the loose ball and Smith headed in.
McGoldrick couldn’t keep his shot down as Town threatened a second almost immediately, Wood linking up well with Cook at the other end but Smith clearing the danger as Blues went into the break ahead.
Silvestri was called into action as the second-half got underway, smothering the danger from Murphy’s drilled cross, then holding onto Maitland-Niles’ first time strike from the edge of the box.
Blues continued to carry the greater threat and Fraser weaved his way past three defenders - and possibly could have had a penalty - before testing Silvestri at his nearpost.
Gerken gathered from Charlie Taylor, then Fraser forced Silvestri into another save, McGoldrick wide with a left foot strike as Blues pressed for that crucial second goal.
Silvestri saved from McGoldrick as the shots on target tally climbed, Cook unable to test Gerken as Leeds looked for a response.
Fraser was a constant problem for the home defence, the Bournemouth loanee firing just wide, Murphy then heading over.
Cole Skuse limped off to be replaced by Giles Coke for the last 15 minutes, Fraser - who looked to be suffering with cramp - also making way for Jonathan Parr, the Norway international yellow carded inside 20 seconds.
Leeds saved their best moments of the game for the closing stages, Cook wide with a right foot effort after the hosts had enjoyed some pressure on the Town defence.
The home side claimed a penalty when Sam Byram went down under Jonas Knudsen’s challenge but referee James Adcock booked the Leeds player for diving as Blues held on for a deserved win and a first success at Elland Road in 10 years.