Bradford threatened from the opening minute and dominated much of the game, but in the end needed a late goal to clinch victory.
The Bantams could have gone in front after only two minutes, when a long-range shot from Joe Colbeck produced an excellent save from Lincoln keeper Alan Marriott.
Lincoln hit back with Gary Croft picking out Mark Stallard with a cross from the left. The former Notts County striker hit a first-time shot, which curled narrowly wide.
Lincoln broke the deadlock in the 26th minute with a controversial goal. Bradford's defence failed to clear a corner with Dany N'Guessan firing in a shot which was blocked on the line.
The ball came out to Louis Dodds, whose powerful effort went through a crowd of players and appeared to be blocked by a defender, but the referee's assistant ruled the ball had crossed the line and the goal was given, despite Bradford's protests.
The speedy Omar Daley set up Bradford's equaliser nine minutes later when he outpaced Ryan Amoo down the left, before cutting in and drawing the keeper. Daley then laid a simple pass back to Guylain Ndumbu-Nsungu, who scored from six yards.
Two minutes later, Peter Thorne beat Marriott again from 20 yards, only to see his effort ruled out for offside.
Lincoln's best spell came in the early part of the second-half, with Dodds having a shot superbly saved by Donovan Ricketts.
Ricketts was beaten in the 67th minute by Lincoln's Lee Frecklington, driving in a shot from 20 yards, but Bradford were saved by the post.
The winner came in the 79th minute, when Lincoln were caught out pushing forward. Ndumbu-Nsungu broke down the middle, before slipping a pass to Colbeck, who went on to score his first goal for Bradford.
Lincoln tried to hit back with a flurry of late attacking, but the Bradford defence held out.