Seth Johnson put Leeds ahead, volleying in from the edge of the area after QPR failed to clear Gary Kelly's corner.
Leeds were reduced to 10 men in the 70th minute when Shaun Derry was shown the red card for violent conduct.
Gallen found the net from a pass by Shabazz Baidoo, then wasted a chance to win it before Adam Miller was dismissed for a second bookable offence.
QPR manager Ian Holloway
"Marc Bircham swears he was brought down and it looked that way.
"I'd have been devastated if we had lost that game and I can't thank my players enough for the attitude they have shown - we deserved something."
QPR: Day, Bignot, Shittu, Rose (Edghill 75), Padula, Miller, Bailey (Baidoo 80), Bircham, Cook, Gallen, Furlong (Cureton 35).
Subs Not Used: Cole, Kanyuka.
Sent Off: Miller (90).
Booked: Bailey, Miller.
Goals: Gallen 85.
Leeds: Sullivan, Kelly, Carlisle, Gregan, Gray, Derry, Einarsson, Johnson (Spring 89), Lennon (Richardson 64), Hulse, King (Pugh 65).
Subs Not Used: Wright, Kilgallon.
Sent Off: Derry (71).
Booked: Hulse.
Goals: Johnson 24.
Att: 18,182
Ref: R Olivier (W Midlands).