Gallen put Rangers ahead in the 11th minute with his fifth of the season and his first since October last year.
He turned past Jody Craddock just inside the area to beat Michael Oakes with a low shot into the right of the net.
Two minutes earlier Paul Furlong drew Oakes into a fine near-post save after Lee Cook curled the ball in from the left.
Wolves were the first to warm up in the freezing, snowy conditions and Leon Clarke went close from a Seol Ki-Hyeon cross in the eighth minute.
The visitors had a chance to equalise on 36 minutes when Lee Naylor's cross met Seol, who was kept out by a point-blank Royce save.
Hoddle still thinks Wolves can make it to the play-offs despite his side beginning the game in 18th place.
Furlong came close to capitalising on Oakes' and Joleon Lescott's dangerous mix-up but was kept out by a last-ditch save from the keeper.
Rangers' Georges Santos was lucky to remain on the pitch after dragging down Colin Cameron, having been booked earlier for a foul on Kenny Miller.
Furlong was could have doubled QPR's lead in the 58th minute but his shot took a deflection off Craddock for a corner.
And Gallen came close to adding to his tally nine minutes from time but his long-range shot was safely gathered by Oakes.
Cort came agonisingly close to equalising for Wolves six minutes before the final whistle when his shot bounced off a post only to be stopped on the line by Royce.
A minute later Royce was not so lucky when sub Cort blasted in Wolves' leveller.