Blues dominated in the first 45 minutes and Carl Motteram opened the scoring ten minutes into the game with a good finish from a Barrowman through-ball.
Twenty-five minutes later and the same two players combined again, Motteram doubling his and Blues tally to make it 2-0.
Clinton Morrison made it 3-0 to Blues twenty minutes after the half-time break when he capititalised on an error by Leeds keeper Carson.
Morrison then handed Leeds a lifeline by giving away a penalty five minutes later after a clumsy challenge on Simon Johnson in the penalty box.
The same Leeds player scored from the resulting spot-kick to bring the score back to 3-1.
Motteram almost grabbed his hat-trick moments before the final whistle but his left foot shot was well saved by Carson as Blues ran-out comfortable winners on the night.
Blues: Vaesen, Kenna, Williams, O'Brien, Purse, Tebily, Hughes, Kirovski, Morrison, Barrowman, Motteram. Subs: Doyle, Painter, Cottrill, Curtis, Alsop.
Leeds Utd: Carson, Krief, McDaid, Keegan, Edwards, Tyrrell, Simon Johnson, Winter, Armstrong, McPhail, McMaster. Subs: Stiens, Wilberforce, Smith, Constable, Shields.
