After seven minutes Courtney Pitt fed the ball to Andy Morrell who struck an angled drive from 16 yards, but Alan Combe made a comfortable save to deny him.
Bradford hit back on ten minutes when Andy Gray set up Windass with a knock down, but the midfielder could not keep his rasping 25-yarder down.
At the other end Steve Staunton whipped over a dangerous cross from the left, but luckily for the Bantams, Morrell could not get his head to the ball as it flew across the face of the goal.
Windass almost opened the scoring for Bradford after striking a sweet right-foot volley from 14 yards, but Gavin Ward did well to take the sting out of the shot.
Bradford were by now playing with more confidence and could have broken the deadlock after a slick move.
Paul Heckingbottom pierced the Sky Blues' back line with a crossfield pass to Gray on the right. The striker ran into the box and put the ball across for Gareth Farrelly, but he fluffed the opportunity with a mis-kick.
Moments later Bradford were almost made to pay for that miss when Julian Joachim found space down the right and whipped over a cross. Morrell met it with a firm header, but he somehow put his effort over the bar.
Bradford were let off the hook and then capitalised by scoring themselves after 34 minutes. Windass ran on to a loose ball and drilled a low shot into the bottom right-hand corner.
Bradford came close to doubling their lead when Farrelly's cross was met by a diving header from Gray at close range, but Ward pulled off a fine block.
Coventry almost levelled less than 60 seconds after the restart when Joachim made a burst down the right and surged into the box to fire a low angled shot but he could only find the sidenetting.
As Coventry pushed and probed for an equaliser, the game threatened to boil over with four bookings in seven minutes.
By and large Coventry were firmly in control and they should have hauled themselves back into the game after winning a penalty on 74 minutes when Mo Konjic was adjudged to have been brought down by Peter Atherton.
Staunton stepped up to hit the ball from the spot, but he blasted his left-foot strike over the bar.
In a grandstand finish Konjic went close for the Sky Blues and Combe somehow kept out a low cross with an outstretched arm to keep the visitors at bay.