A goal on the stroke of half-time from Richard Keogh and two more in the second half from Scott Dobie and Matty Robson extended Carlisle’s unbeaten run to six games.
Events turned against the Bantams in the 39th minute when defender Simon Ramsden was sent off for a second yellow card, both times for fouls on Carlisle danger man Robson.
Carlisle applied pressure as half-time approached and it paid dividends in the 44th minute when Keogh blasted home the loose ball from six yards after City keeper Simon Eastwood had parried Robson’s skimming low drive.
The hosts finally made it 2-0 midway through the second half. Kevan Hurst played Dobie in to space and the striker, who had only been on the pitch for four minutes, had time to pick his spot and drill the ball low past Eastwood and inside the left-hand post from 10 yards.
Robson made it safe for Carlisle in the 74th minute with a stunning break from halfway. The winger latched on to Vincent Pericard’s clearance from a Bradford corner and evaded two defenders before slipping the ball past Eastwood from the edge of the box.