Owen Coyle's side, fresh from their Carling Cup triumph over Chelsea in midweek, recovered from a poor start to secure a deserved win.
QPR went ahead on 13 minutes, when Dexter Blackstock collected Lee Cook's pass and fired into the bottom corner of the net from ten yards.
Blackstock then had a header from Hogan Ephraim's corner tipped over by keeper Brian Jensen, who also saved a long-range shot from Martin Rowlands.
Cook fired over as the home side continued to dominate, but Burnley equalised against the run of play on 34 minutes.
Joey Gudjonsson's pass found Robbie Blake unmarked and the Clarets forward was given time and space to shoot into the top corner with keeper Radek Cerny helpless.
The goal galvanised Burnley and Chris Eagles went close to putting them ahead with a rasping drive that flew just over, before Cerny saved a shot from Chris McCann.
Burnley continued to put Rangers under pressure in the second half and Wade Elliott should have put them in front, but fired straight at Cerny after being put through by Graham Alexander.
Rangers responded and had strong appeals for a penalty waved away after Blackstock was brought down by former QPR defender Clarke Carlisle.
And when the impressive Eagles was stretchered off, the game seemed to be slipping from Burnley's grasp.
But seven minutes after coming on for Eagles, Mahon smashed home from the edge of the penalty area when Elliott's cross was poorly cleared by Fitz Hall.
Blackstock's header wide from Hall's cross was the closest Rangers came to finding an equaliser, but the visitors held on.