Gary Rowett's side made it back-to-back away wins in the Sky Bet Championship following an impressive 2-0 victory at Elland Road.
Goals from Demarai Gray and a late Jacques Maghoma strike sealed the win for Blues.
It was Gray who mustered up the first effort of the afternoon as early as the seventh minute. After good aerial work from Clayton Donaldson, David Davis picked out the run of Gray, but the youngster dragged his effort across goal and wide of Marco Silvestri's right-hand post.
The home side responded quickly, former Blues loanee Chris Wood chancing his arm not once, but twice, firstly from distance but his effort had the same outcome as Gray's earlier chance; then the New Zealander saw his powerful shot well blocked by Michael Morrison.
After a pin-point switch of play from Jonathan Grounds, Paul Caddis got the better of Leeds left-back Charlie Taylor, before getting his cross over, but unfortunately for Blues, Maikel Kieftenbeld couldn't direct his header goalwards in the twelfth minute.
Blues looked threatening on the counter-attack. Defender Liam Cooper was booked as David Cotterill and Donaldson looked to catch the hosts on the break and from the resulting free-kick, Cotterill's effort was cleared, only as far as Davis, who fired a 25-yard shot narrowly over the crossbar.
Just after the half-hour Blues took the lead. Another swift attack from Rowett's side and after Donaldson was dispossessed on the edge of the area, Gray pounced, picking up the loose ball and taking advantage of Cooper's slip before rifling his shot into the roof of Silvestri's net to claim his first goal of the season.
Moments later, Blues were nearly gifted another chance. After Gray was brought down 30-yards from goal, Cotterill tried his luck again, forcing Silvestri into a save which the 'keeper luckily held at the second attempt.
As the half wore on, Blues frustrated both the Leeds players and fans and Gray went close again four minutes before the interval. His low, curling effort from the edge of the box was beaten away by Silvestri.
The hosts had their best chances on the stroke of half-time. Stuart Dallas almost benefiting from a kind ricochet, only to be denied by a superb save from Tomasz Kuszczak. From the resulting corner, Blues initially cleared but Lewis Cook's drive back into the box looked destined to be turned home by Sol Bamba at the far post, but an important toe from Grounds diverted the ball away from the Leeds captain and Blues went into the break the happier of two sides.
Stephen Gleeson had the first sight of goal three minutes into the second half, but his ambitious volley sailed wide of Leeds' goal after Cotterill's corner was headed clear.
Two minutes later and Leeds had their first effort of the second period. After Dallas pulled the ball back from the left hand-side of the Blues box, Alex Mowatt's tame effort was easily gathered by Kuszczak down low at his near post.
Blues continued to frustrate and Donaldson almost punished Leeds, getting the wrong side of the Leeds back-line, but the striker couldn't find the target.
Ten minutes after the restart and skipper Bamba could have done better when he rose highest at a corner, but his towering downward header fell just wide of Kuszczak's post.
Uwe Rosler introduced Mirco Antenucci just after the hour, which seemed to spark Leeds into immediate action. Antenucci's pass found Dallas, whose cross fell to Cook at the far post and his effort brought another fine stop out of Kuszczal, which initiated another Blues attack. Gray picking the ball up in his own half, running and knocking the ball past the Leeds defence and the Blues goalscorer's cross eventually found substitute David Davis but his effort was stopped on the line.
With the hosts pressing more and more for the equaliser and with a quarter of an hour remaining Rowett introduced Jonathan Spector to try and preserve their slender lead.
The Blues defense had some relief after Kieftenbeld broke with the ball before playing in Donaldson who forced a corner against Cooper. From the corner, Grounds, under heavy marking, couldn't get enough purchase on the ball to trouble Silvestri, who gathered easily.
In the 83rd minute, Morrison made a vital challenge inside his own six-yard to deny Antenucci - for what would have been a glorious opprotunity for Leeds to pull level - allowing Kuszczak to come out and claim.
Five minute later and Kuszczak nearly gifted the hosts the chance they craved. Luke Murphy's free-kick was spilt by the Blues 'keeper but fortunately, Blues scrambled the ball away.
As the fourth official held up the board to indicate the stoppage time, Maghoma sealed the win for Blues. Donaldson again beating Cooper in the air, allowing Maghoma to drive at the Leeds goal before unleashing an unstoppable drive from the edge of the box.
Another fantastic away performance from Rowett's side, who soaked up a lot of Leeds pressure and punished their hosts on the counter-attack.