Andy Cook scored twice as managerless Carlisle suffered a fourth defeat in five Sky Bet League Two games.
Bradford were in front after two minutes as Jamie Walker capitalised on a poor touch from defender Jon Mellish to set up Cook.
Charlie Wyke had already missed a chance against his old club and Carlisle threatened again with Dominic Sadi and Jordan Jones testing home keeper Sam Walker.
Bradford and Cook could have had a second goal after 22 minutes when Richie Smallwood’s free-kick found him unmarked in front of goal. But Cook headed sideways and Olly Sanderson fired over the bar.
The lively first half continued as Mellish made a crucial block to deny another Sanderson shot after the on-loan Fulham striker had burst into the box.
Wyke hit the post for Carlisle before they levelled through Harrison Neal as Walker fumbled his high flick into the net.
Lewis pulled off a double save from Cook and Sanderson but Cook headed Bradford back in front from Tyreik Wright’s cross.
