The 36-year-old, who topped the League One scoring charts last season, stroked home his second of this campaign after referee Paul Robinson awarded the Bantams a 27th minute penalty following Ben Chorley's challenge on Andy Cooke.
The Dons skipper looked to have caught Cooke's heels as he lined up to drive home a Marc Bridge-Wilkinson cross, but Mr Robinson only pointed to the spot after the intervention of his assistant.
There were then more discussions with both touchline officials before the referee piled on the misery for the Dons by red-carding Chorley.
Windass coolly finished from the spot and the early goal provided a much needed lift for the home side following their dismal defeat to Southend on Tuesday.
With tricky winger Ben Murihead providing a constant threat, Bradford's attacking play clicked into gear and Windass will be kicking himself after he wasted a host of clear-cut chances.
Soon after his opener Windass clipped the outside of a post after being put clean through on goal and five minutes before the break his header was saved by Matt Baker.
In the last minute of the half Windass headed home from close range after another great cross from Muirhead, but this time he was flagged offside.
The Dons attack got little reward out of Bradford's solid back four and midfielder Wade Small wasted a great chance to equalise in injury time when he miscued a shot from 14 yards out.
Muirhead, who was making his first start of the season, provided the ammunition for Windass' second after 52 minutes when Cooke left his low cross and his strike-partner fired home from close range.
With the Dons barely able to launch an attack it was just a question of whether Windass would bag a hat-trick.
After 62 minutes he should have taken advantage of a mistake by Baker, but instead found the side-netting and when substitute Danny Cadamarteri laid on another chance 19 minutes from time Windass completely scuffed his shot from six yards out.
The Dons, who had won on three of their last four visits to Bradford and scored 15 goals, plugged away against the odds but they only tested keeper Donovan Ricketts late on when Izale McLeod fired in a curling shot after tricking his way into the box.