Coventry scored in the first minute at Valley Parade, but Bradford equalised and the Sky Blues could not force another chance home.
Gary McAllister got the early goal for the in-form visitors, after more super work from teenager Robbie Keane.
Lee Mills equalised with two minutes of the opening period to go, inspired by first half substitute Peter Beagrie.
Coventry left Yorkshire having extended their unbeaten run to a creditable seven matches.
But they missed a hatful of second half chances and will be unhappy not to take all three points back to the Midlands.
Seconds to score a goal
It took McAllister just 43 seconds to score for a side which had netted four times in two of the last three games.
It was a simple goal as the Bradford defence gave McAllister the freedom of Valley Parade to poach his seventh goal of the season.
The Coventry skipper started the move with a ball to Robbie Keane out wide on the left.
He continued his run by ghosting into the heart of the Bantams area as Keane sprinted forward and crossed into the path of the unmarked Scot.
Surprise England call-up Steve Froggatt was watched by national coach Kevin Keegan and produced a dazzling opening 15-minute spell for the Sky Blues.
The latest left-sided England hope twice tried to supply Keane but Matt Clarke produced the first of a number of fine saves for Bradford.
Bradford were non-existent as an attacking force until the 40th-minute introduction of Peter Beagrie, back from a hip injury.
Bradford hit back
Mills then unluckily hit the bar with a stunning chip over Magnus Hedman from 18 yards, before leaving the Swedish keeper helpless just before the break.
Beagrie was the architect, turning Paul Telfer inside out before delivering a far-post cross to Mills to chest down and volley from six yards for his fourth goal in five games.
David Wetherall made a stunning block from Mustapha Hadji before half time, and volleyed over from an even better position deep into injury time.
Fantastic Clarke
While Beagrie continued to inspre Bradford after the break, it was Coventry's Moroccan duo of Hadji and Youssef Chippo who had the majority of the chances.
But Clarke was equal to anything on target from them, and from Keane and Carlton Palmer.
The woodwork saved Bradford on two occasions, with Keane's effort pushed onto the post and then rolling along the goal-line.
Hadji did have the ball in the back of the net just over 13 minutes from time, but while the players and fans celebrated in earnest the linesman's flag had been raised all the time.
Four minutes of injury time was promised by the officials and their electronic board, although for some reason referee Barry Knight chose to play only half that time, as both sides sought a winner.
Teams:
Bradford: Clarke, Halle, Wetherall, O'Brien, Sharpe, Windass, McCall, Redfearn, Saunders, Mills, Blake. Subs: Walsh, Lawrence, Beagrie, Rankin, Dreyer.
Coventry: Hedman, Williams, Shaw, Telfer, Hall, Chippo, McAllister, Palmer, Froggatt, Keane, Hadji. Subs: Ogrizovic, Burrows, Breen, Eustace, Roussel.
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