Ian Harte, recalled at left back in place of Teddy Lucic, who was suffering with a tight hamstring, challenged Paul Devlin who stumbled inside the penalty box.
Referee Phil Dowd waved play on and two minutes later Leeds showed their power in the air to open the scoring.
Gary Kelly sent a high cross from the right to the far corner of the six-yard box where Viduka beat Jeff Kenna in the air. The Australian striker nodded the ball inside to Norwegian Eirik Bakke who had the simple task of heading his first Premiership goal of the season.
Injury-hit but full of spirit, Birmingham responded by going close several times. Damien Johnson was denied by Paul Robinson's fingertip save and later by Kelly's goal-line clearance.
Leeds also somehow survived as the ball pinged around the goalmouth with no Birmingham player able to get a decisive touch.
Birmingham had another penalty claim rejected early in the second half when Danny Mills made what looked a fair tackle on Clinton Morrison.
Nico Vaesen saved well from the hard working Viduka, who was eventually rewarded in the 67th minute, heading his sixth goal of the season at point blank range, with Kelly the provider.
Teenage sensation James Milner replaced Bakke with 17 minutes left as Leeds coasted home.