The former Manchester United man single-handedly dragged his new side back into the game and they look good outside bets for promotion.
The hosts had won three of their last four games, while Burnley were reeling after drawing at home to bottom-of-the-table Colchester in their last outing.
On 14 minutes the hosts took the lead thanks to Gavin Mahon - one of seven January signings in the starting line-up - who headed in his first for the club.
The goal was down to the industry of Akos Buzsaky, who superbly worked space in the corner with Patrick Agyemang, before swinging in a cross that Mahon could not miss.
QPR won the first meeting between these sides 2-0 back in December and that result looked on the card again when Agyemang scored for the sixth successive game.
The former Preston man took full advantage of a superb run and through-ball from left-back Damien Delaney to coolly round keeper Brian Jensen and slot home.
QPR were completely in command but Cole, who wasn't getting a game under Roy Keane at Sunderland, dragged Burnley back into the match with a true poacher's effort when he deflected Joey Gudjonsson's free-kick past Lee Camp just before half-time.
And Cole scored his second ten minutes after the break when he smashed Ade Akinbiyi's cross in off the bar as the home defence went missing.
Rangers appeared stunned and were forced into last-ditch defending as Burnley played cleverly on the break.
Wade Elliott rattled the post from fully 25 yards with Camp grasping at thin air.
And unbelievably Burnley were ahead when Akinbiyi headed home after Kyle Lafferty lofted a hopeful ball back into the QPR area.
Then with QPR chasing the game, Cole added the icing onto the cake by heading home Elliott's cross for his fourth in two games for his new club.