The visitors struck against the run of play when new boy Remy latched on to an inch-perfect Adel Taarabt through ball and slotted past Jussi Jaaskelainen on 14 minutes.
The Hammers' equaliser came in the second half when substitute Carlton Cole saw his header parried into the returning Joe Cole's path who tapped in the much-deserved leveller - his first for the Hammers since 2003.
The hosts started the better side and looked towards Marouane Chamakh through almost hopeful long-range passes at times.
But, as these tactics continued, QPR kept exploiting the pace of Remy with Taarabt picking the striker out every time with a pass and only the offside trap stopping the 26-year-old in his tracks.
The passes soon paid off when Taarabt threaded a defence-splitting ball towards Remy who had timed his run and steadied himself before coolly finishing for the opener and a dream start to his Premier League debut in the 14th minute.
A shell-shocked West Ham could have got back into the tie when Chamakh shook off a Clint Hill hold before going down under a Shaun Wright-Phillips challenge in the area but Webb was not convinced by the Morocco international's pleas.
It was not until the second half that the hosts really took hold of the game with Mohamed Diame seeing a shot on the turn blocked and Matt Jarvis' teasing crosses from the left failing to have an end product.
QPR had little to shout about after the break as they were made to defend which they did resiliently until the equaliser in the 68th minute.
It came from a delicate delivery from Jarvis, who had been locked in a tasty battle with Nedum Onuoha all afternoon, and the rising Carlton Cole headed down, forcing Cesar to save to his left. However, the Brazilian's block fell kindly into Joe Cole's path and he had the easiest of finishes to see Boleyn Ground erupt.
Winston Reid then had a piledriver blocked expertly by Stephane M'Bia who was in fine form throughout, putting his body on the line at every opportunity and gratefully seeing a goalmouth scramble cleared.
Joe Cole was then forced out wide by Cesar in the area with the midfielder managing to get his shot away after rounding the keeper, however Fabio was in the right place to clear from the line.
QPR held on for what could be a vital point for their fight for survival, with West Ham unable to make their chances count.