Although Stuart McCall's men collected their fourth clean sheet on the bounce they were out of luck in front of goal against a hard-working Darlington side who were playing their first game since January 31.
Former Huddersfield Town man Pawel Abbott posed most of the threat to City's back-line, but in a disappointing first half it was Bradford who came closest to breaking the deadlock.
After 16 minutes Bantams striker Michael Boulding wasted a lucky bounce of the ball when he fired straight at keeper Dean Gerken and, on the half-hour mark, leading scorer Peter Thorne saw his improvised shot rattle the Darlington crossbar with Gerken flat-footed.
But City's game plan was disrupted when Jamaica international Omar Daley was stretchered off with a leg injury after a heavy challenge early on and Darlington's battling midfielders did well to stifle Bradford's in-form playmakers Nicky Law and Dean Furman.
City's injury worries increased when keeper Rhys Evans pulled a muscle trying to stop a corner and the Bradford shot-stopper did well to last the remaining hour of the game.
In truth however Darlington failed to put enough pressure on the City keeper and it was not until late on that he was called into action to tip over a goal-bound volley from Abbott.
Former Darlington man Matt Clarke produced some crucial blocks to protect his injured keeper, but it was only in the closing stages that Darlington built up some pressure.