Three goals in nine minutes from new signing Mark Yeates, who joined the Bantams from Watford, last season’s leading scorer Nahki Wells and James Hanson midway through the first half settled the contest.
Yeates opened the scoring after 20 minutes, taking a pass from Garry Thompson on the left before side stepping inside right-back Brad Potts and beating goalkeeper Mark Gillespie with a superb angled shot into the far corner.
Wells added the second five minutes later when he chased a headed pass from visiting skipper Paul Thirwell that was intended for Gillespie and taking the ball round the stranded keeper.
Hanson scored the third after 29 minutes, evading Danny Livesey as the Carlisle defender stumbled and scoring with a low right-footed shot to give Bradford a 3-0 half-time lead.
Skipper Gary Jones scored the fourth in the 66th minute after Wells had squared the ball into his path.
Carlisle, who have conceded nine goals in their first two league matches, rarely troubled Bradford keeper Jon McLaughlin.