Veteran midfielder Stuart McCall thanked his former club with a right-foot strike, but Windass added to his side's misery with a needless red card in the dying seconds of the game.
McCall's winner lifted the Blades to the top of the table ahead of Wigan's match at Coventry and extended their remarkable unbeaten run against City to 15 matches.
But Windass, who opened his account for the season, ruined his day by collecting a red card with virtually the last kick of the game.
Windass had plenty to prove to Blades boss Neil Warnock after he was left out of the play-off final last season and City manager Nicky Law pulled an early surprise by giving the striker a midfield role.
It looked like being a masterstroke as Windass posed problems early on and he saw a ninth minute header fly just over the Blades bar.
McCall carved out an opening for team-mate Michael Tonge after 21 minutes but City centre-half Jason Gavin made a vital block to clear the danger.
Just before the half-hour Windass got the goal he desperately wanted when Jon Harley's poor headed clearance fell at his feet and he drilled a low right-foot drive past Paul Gerrard from 16 yards.
In City's next attack striker Michael Branch was clipped by Mike Whitlow but referee Paul Taylor waved away Bradford's penalty appeals and within seconds, in-form Peter Ndlovu had levelled with a stunning strike.
Some sloppy work by Gavin contributed to City's downfall but when the ball sat up for the Zimbabwean he unleashed a fierce right-foot screamer from the edge of the box.
The setback failed to upset City's composure and it took a desperate goal-line clearance from Rob Kozluk to deny Windass a second from a close-range header.
At the start of the second half Blades keeper Gerrard brilliantly saved an Andy Gray volley and the tide turned Sheffield's way when McCall coolly fired them in front from just inside the Bradford box.
Paul Evans almost equalised with an overhead kick but the final act was Windass scything down Michael Brown as he sprinted down the touchline and referee Taylor showing him the inevitable red card.
Bradford: Beresford, Edds, Wetherall, Heckingbottom, Emanuel, Summerbee, Evans, Branch, Gavin, Windass, Gray. Subs: Paston, Francis, Muirhead, Wolleaston, McHugh.
Sheff Utd: Gerrard, Kozluk, Jagielka, Whitlow, Harley, Tonge, Montgomery, McCall, Brown, Ndlovu, Ward. Subs: Allison, Peschisolido, Lester, Armstrong, Cryan.
Referee: P Taylor (Hertfordshire).