Veteran striker Jamie Cureton struck his 13th goal of the season to give Exeter victory over Bradford.
The 37-year-old swept in Matt Oakley's nod-down to score the only goal of the game before half-time.
Bradford came back strongly after the interval, but Alan Connell's shot was cleared off the line and Garry Thompson's strike went wide.
The Bantams also wanted a penalty when Nahki Wells went down in the area, but the referee waved appeals away.
VIEW FROM THE DRESSING ROOM
Exeter City manager Paul Tisdale told BBC Radio Devon:
"I happen to think one-nil is exactly what we needed, it just shows to the players they can grit out 50 minutes of very threatening football.
"That's us at our best away from home.
"I went defensive but I'm not ashamed of that. We stuck it out and I think our physio is going to have a tough couple of days, we've got four or five players who are bruised and battered.
"We stuck it out, we got to the ball, it wasn't pretty but we did what we had to."