QPR's on-loan Tottenham forward Adel Taarabt twice combined well with Wayne Routledge early on, only to be denied by keeper Paul Rachubka.
And Rangers should have gone ahead when Routledge breezed past Stephen Crainey and sent in a low cross towards Heidar Helguson, who scuffed a shot against the crossbar.
Helguson then missed another good chance, steering the ball wide of the near post after being picked out by Martin Rowlands.
Rangers were punished for those misses when Charlie Adam's ball into the box was laid off by Gary Taylor-Fletcher to Burgess, who fired through Ramage's legs and into the bottom corner.
In the second half Rachubka clawed away Fitz Hall's looping header and Keith Southern blocked Angelo Balanta's attempt to force home the rebound.
QPR crowd favourites Akos Buzsaky and Rowan Vine came off the bench and Buzsaky went close with a long-range free-kick.
Rangers struggled to create chances though and were dealt another blow when skipper Rowlands - recently back from knee ligament damage - hobbled off with another injury.
The points looked safe for Blackpool when Vine hopelessly shot wide after fellow substitute Patrick Agyemang's left-wing cross found him in space.
But with four minutes remaining, Ramage trotted down the right flank and sliced the ball into the net.
And Taarabt missed an opportunity to win the match for Rangers when he headed Routledge's late cross wide of the target.