United took command early on and were two up at half-time, and they made their superior numbers tell with three more after Bradford's Gus Uhlenbeek was sent off early in the second half.
And veteran Windass made it two when he struck a shot past Myhill from just inside the penalty area five minutes from the break after a pass from Kabba.
United manager Neil Warnock could not have asked for more from his new duo, with former Bradford favourite Windass also making his debut on loan from Middlesbrough.
The agony was not over for the dispirited Bantams as former Blade Uhlenbeek was red-carded for a bad foul on Michael Tonge after 56 minutes.
And just three minutes later the visitors' central defender Shaun Murphy headed the third from Michael Brown's cross to kill off the game.
Brown then stepped up to convert an 80th-minute penalty, striking a right-foot shot past Myhill after Andy Myers had fouled Tonge, to make it four.
And substitute Carl Asaba completed the rout when he shot home from John Paul McGovern's cross two minutes from time, just after heading another chance over the bar.
He had threatened to score even before his goal, twice putting the ball wide with close-range efforts, and he also went desperately close when his shot cleared the bar in the second half.
Struggling Bradford, with an entire team sidelined through injury and suspension, could make no impact as they sought to improve on a record that has seen them win just once in their last 12 games. They looked woefully weak and rarely threatened Paddy Kenny's goal, with a long-range shot from Uhlenbeek and a Delroy Facey effort both going wide in the first half, and a shot from Juanjo calling Kenny into belated action after the break.
United were much livelier as they ended a four-game winless streak in the league with a rampant performance.