The Grecians went in front after 11 minutes when Craig Woodman swung a corner towards goal and although goalkeeper Matt Duke got a touch, the ball went through his hands and into the net for an own goal.
Bradford barley posed a threat in the first half and Exeter doubled their advantage in the 45th minute, Jake Gosling crossing for Lawson D'Ath to head in at the back post on his Grecians debut.
Bradford upped the ante after half-time and the pressure they were applying reaped its reward when they pulled one back with an almost identical goal to Exeter's opener.
Kyel Reid's corner swung dangerously towards goal and Artur Krysiak could not get near it as the ball ended up in the net, with the substitute credited with the score.
However, the Grecians wrapped up the points almost immediately, Scot Bennett letting fly from distance and the ball flew past Duke, with the aide of a slight deflection, and into the net from fully 25 yards.
John O'Flynn added the fourth after 89 minutes when he tapped in after some unselfish play by Mark Molesley.