The 20-year-old midfielder, who only learned he was playing when Andrew Impey reported sick an hour and a quarter before kick-off, met Trevor Sinclair's corner on the edge of the area and scored with an inspired, controlled volley off the outside of his left foot.
It was a rare moment of achievement in a Rangers performance that was generally as meagre as the crowd - 7,776, the lowest at Loftus Road for a decade.
"We know we have to play better than this to get up the table," Houston said. "But it was a good time to score."
It was, from Bradford's point of view, a cruel time to score. Until that moment a side which included the 37-year-old midfielder Gordon Cowans and two 35-year-old forwards in Carl Shutt and Chris Waddle, had looked well worth a point.
Brazier's glowing moment apart, the evening's most warming moments were provided by Waddle's elegant embellishments. The former Newcastle, Marseille and Sheffield Wednesday winger, on a month to month contract, had one of Bradford's better chances after just 12 minutes but wafted a shot over the bar. His colleagues, Andy Kiwomya and Shaun Murray, also missed decent opportunities to set Rangers back.
But until Brazier's triumph of youth over experience, the nearest Rangers had come to a goal was a sliced clearance by Bradford's 17-year-old defender, Andrew O'Brien.
Rangers, who badly missed the injured Daniele Dichio up front, are still searching for new players. "The hunt's going on," Houston said. "Anything imminent?" someone asked. "We are still in a fact-finding situation," he replied gravely. Life gets hard when you slip out of the Premiership.
Queen's Park Rangers (4-4-2): Sommer; Graham, McDonald, Ready, Brevett; Sinclair, Barker, Murray, Brazier; Slade, Charles. Substitutes not used: Plummer, Perry, Roberts (gk).
Bradford City (4-4-2): Nixon; Lidurd, O'Brien, Mohan, Jacobs; Duxbury, Cowans, Murray (Pinto, 77), Kiwomya; Waddle, Shutt (Stallard, h-t). Substitute not used: Midgley.
Referee: C R Wilkes (Gloucester).Reuse content