Cup kings Bradford finally ran out of steam as Exeter came and took all three points on their visit to West Yorkshire.
Much-travelled striker Jamie Cureton struck his 13th goal of the season to give Exeter maximum points.
The 37-year-old swept in Matt Oakley’s nod-down to score the only goal of the game before half-time.
Bradford - who were playing their 25th game and are still alive in three Cup competitions as well as the League Two promotion race - came back strongly after the interval.
Alan Connell had a shot cleared off the line and Garry Thompson’s strike went wide.
The Bantams also had a penalty appeal, after Nahki Wells went down in the area, waved away.