The Bantams striker bagged only his second goal of the season in dramatic fashion, but the result was still overshadowed by the fact that the match marked the first league meeting between the two sides since the Bradford fire disaster in 1985 which claimed 56 lives.
After a moving tribute to those who died, Stuart McCall's men got off to just the start they wanted when frontman Peter Thorne drove home the opener after just a minute.
Right winger Joe Colbeck open up the visitors defence with a determined run and, when his fierce cross reached Thorne, the Bantams striker controlled it superbly before firing home a right-footer from 12 yards.
Lincoln manager Peter Jackson, who was the Bantams skipper on the day of the fire, had to shuffle his line-up when winger Dany N'Guessan limped out of the action after just six minutes, but despite the early setback his side looked threatening up front.
Striker Ben Wright had his cool finish ruled out for offside and substitute Mark Stallard saw his curling 25-yard shot brilliantly pushed round the post by Bradford keeper Donovan Ricketts.
Wright, who was a handful for the Bradford defence, came close to levelling after 25 minutes when his goal-bound header was scrambled off the line, but Thorne should have doubled the home side's tally soon after.
Thorne was picked out superbly by Kyle Nix's cross but, with time to control and finish, the striker guided the ball tamely into the hands of keeper Ben Smith.
The hard-fought contest boiled over just before the break when Lincoln skipper Scott Kerr was booked for his ugly challenge on Nix and Bradford midfielder Paul Evans was cautioned for his intervention.
Six minutes after the restart the visitors drew level through 18-year-old winger Lenell John-Lewis who marked his first start with a crisp finish.
Bradford's defence failed to clear a high ball and when it was laid back into John-Lewis' path he beat Ricketts from 16 yards with a fierce right-foot shot which bounced down off the crossbar.
With a draw looking the most likely result, Bradford staged a late rally and they snatched a first league win since mid-November thanks largely to a scintillating run from winger Omar Daley.
The Bradford speedster out-paced his marker on the right and, after he calmly pulled the ball back from the dead-ball line, Conlon managed to get enough power in his shot to beat a wrong-footed Smith.