Alan Connell's late volley saw off 10-man Torquay and moved Bradford up to fourth in League Two.
The home side dominated early on and saw their chances of victory improve when Gulls skipper Brian Saah was sent off for elbowing James Meredith.
Both sides hit the woodwork in the first half and Torquay stopper Michael Poke made a string of fine saves to keep the sides level.
But substitute Connell's brilliant late strike sealed the points for Bradford.
VIEW FROM THE DRESSING ROOM
Torquay United manager Martin Ling told BBC Radio Devon:
"It was backs against the wall, we stuck at it but it took a wonder goal to beat us.
"It was a poor cross but a wonderful finish and that cost us the game. It would've been a valuable point but it was not to be.
"After the sending off we went 4-3-2 but by the time we had ran around trying to regain the ball we couldn't retain it. When it's 11 v 10 it was always going to take it out of you."