The Bantams put their recent poor form behind them and took the lead after just two minutes. A dreadful mix-up in the Lincoln defence left James Hanson with a simple tap in and the striker made no mistake from five yards.
Lincoln, playing their first game in five weeks, drew level against the run on play in the 22nd minute when referee Mark Brown controversially ruled that Gareth Evans handled inside the box and Ashley Grimes sent the keeper the wrong way from the resulting spot kick.
Bradford scored what proved to be the winner in the 41st minute when Gareth Evans held off two defenders before firing spectacularly into the net from the edge of the box.
Lincoln piled on the pressure in the second half but could not find a way through.
Adam Watts had a shot blocked and then veteran Delroy Facey saw a powerful effort deflected over. Watts went close again six minutes from time when his close range effort was blocked on the line.