The game was turned on its head at the end of the first-half as first Windass showed that he has lost none of his cunning as he curled home a quick free-kick.
As the home fans were still celebrating on-loan forward Graham marked his home debut with his first goal in Bradford colours.
Bradford made a dreadful start conceding the opening goal after just 74 seconds when Craig Woodman swung over an inviting cross from the left flank. Young full-back Ben Parker was left exposed on the far post leaving Scott Murray to steal in to steer a header past Donovan Ricketts.
Bradford had more of the ball in the opening period but had failed to really test Adriano Basso.
Bristol probably thought they had done enough to earn the half-time lead, but the game was quickly turned around when Louis Carey got involved in a tussle with Windass on 41 minutes. The Bristol defender was booked and Windass added to his woes by slotting the resulting free-kick into Basso's right-hand corner as he was still organising his wall.
But worse was to follow for the visitors just a minute later as Graham opened his account when he latched on to David Cotterill's miss-placed pass. He surged goalwards before unleashing a shot which deflected off the unfortunate Carey and beyond Basso.
In an entertaining second period both sides pushed forward and another new Bradford signing, Jermaine Johnson, twice went close to opening his account.
But it was his fellow Jamaican international Ricketts who was Bradford's hero in the end producing two fine saves to deny Bristol an equaliser.
He firstly tipped David Noble's gold bound effort wide before using all of his giant frame to deny Noble again finger tipping over the bar.
One worry for the Bradford fans was the sight of skipper David Wetherall limping off early in the first-half.