The Millers striker put them two ahead with a finish of real quality and, although a harsh penalty decision gifted City a late lifeline, the South Yorkshire outfit fully deserved their long-awaited victory.
The visitors sacked manager Mick Harford after last weekend's defeat at home to Yeovil, but they looked the side full of confidence as Bradford struggled to shake off their FA Cup hangover.
The Bantams were dumped out of the cup on home soil by Barnsley and they again faltered in front of their own fans.
Burton showed his intent early on with snap-shot from the edge of the box and soon after he almost embarrassed the City keeper with a quick-thinking strike from 30 yards which clipped the Bradford bar.
Millers skipper Colin Murdock was in commanding form throughout and he was unlucky when his powerful header struck the City bar, but it was only a let-off for the home side.
As Bradford failed to deal with the rebound the ball fell to midfielder Lee Williamson and he hit a superb 20-yard strike to notch up his first league goal since February 2002.
City's striker Dean Windass wasted a great chance when he headed wide after 24 minutes and just after the break his downward header was pushed over by Millers keeper Neil Cutler.
After an hour Burton showed his class when he bamboozled the City defence with a neat flick on the edge of the box before he drilled a superb 20-yard strike beyond keeper Russell Howarth.
City have now lost six times in 13 games at home and they never looked like getting back into this contest until referee Phil Josplin ruled that full-back Gregor Robertson had handled a cross by Danny Cadamarteri.
Windass calmly fired home the spot-kick, but referee Josplin made him take it again for encroaching. The striker held his nerve to again send Cutler the wrong way, but the goal failed to spark the Bantams into life.
Another hopeful penalty appeal was waved away by the referee and substitute Steve Claridge headed a late chance wide to cap a miserable week for the Bantams.