Mahon, who will join the Clarets in a permanent deal from Wigan at the end of the season, was head and shoulders above everyone else with his all round ability.
Mahon created the only goal 11 minutes from time with a neat turn and pass into the path of striker Andy Gray who converted in style past veteran Wales international keeper Paul Jones for his third goal since joining from Sunderland.
The combination of Gray and Mahon also created the first half's only real opportunity with Jones using all his large frame to touch a shot from Mahon behind for a corner.
The game generally had an end of season feel to it with the lively Mahon doing his best to raise the temperature on a bitterly cold afternoon.
Rangers skipper Gareth Ainsworth provided a rare moment of danger for the home defence as his burst into the penalty area in first-half stoppage time was halted by a brave save from Brian Jensen.
Mahon began the second half with a 30-yard drive which tested Jones to the full, while at the other end Ainsworth turned provider for Marc Nygaard whose effort was kept out by Jensen.
Burnley boss Steve Cotterill withdrew striker Michael Ricketts in an attempt to give Mahon more of the possession and this was to prove a match winning substitution with the winger creating the winner for Gray.