The powerful Irishman came off the bench and showed plenty of grit as he ran in to head home a hanging ball after skipper Graeme Lee saw his fierce free-kick rattle the Bury bar.
The visitors were far from happy about Conlon's full-blooded finish as keeper Wayne Brown waited to claim the awkward rebound with just five minutes left, but City did just enough to shade the win in a hard-fought battle.
Bury went into the match without having lost in the league on their travels and they showed some neat touches early on as City struggled to find their rhythm.
There was little goalmouth action to warm either set of fans during the early exchanges, but City finally clicked into gear after Michael Boulding's snap-shot flew inches wide from the edge of the Bury box.
Bantams' striker Peter Thorne then headed wide before the visitors were almost gifted an opener by keeper Rhys Evans's miss-hit clearance.
The City stopper did well to cover Andy Bishop's break from half-way, but when his scuffed kick fell to Elliott Bennett the Bury winger failed to hit the unguarded net from 40 yards.
Loan signing Nicky Law should have marked the start of his second spell with City by firing them ahead after 27 minutes but the midfielder miscued his left-foot shot from eight yards after great build-up play by Omar Daley and Boulding.
Evans rode his luck again on the half hour when Bury midfielder Stephen Dawson beat him with a curling 20-yard shot which hit the post and then bounced out of play off the City keeper's back.
Both sides stepped up the tempo after the interval, but it was almost a bizarre mix-up which handed City the lead.
Bury centre-half Cresswell beat his own keeper with a wayward back pass, but Brown did superbly to race back to his goal and push the ball off his goal-line.
Evans tipped over a far post header from Efe Sodje in a rare Bury attack, but with the fireworks going off around the ground Conlon's arrival set up a frantic finale.
With the visitors' expecting a set-piece move from Paul McLaren, Lee stepped forward to let fly with a rasping drive and with the whole ground waiting for the ball to drop Conlon took charge to break the deadlock.