Shabazz Baidoo's controversial late equaliser kept QPR in the FA Cup after a lively third-round clash. Baidoo appeared to handle the ball over the line 14 minutes from time, but after consulting with his assistant, referee Tony Bates gave the goal.
Dexter Blackstock put QPR ahead after 32 minutes from Lee Cook's cross.
Rowan Vine's curling drive seconds before half-time levelled for Luton, and Warren Feeney scored just after the re-start, but Baidoo earned a replay.
QPR boss John Gregory on Baidoo's goal:
"It wasn't just one hand - the ball hit both of them. He put his arms up to protect himself and the ball hit him and ended up in the net. "After that, I think we should have gone on to win it. But it was a game of mishaps and mistakes.
"What we need to do in the replay is try and replicate the way we played in the first 44 minutes."
Luton boss Mike Newell on Baidoo's goal:
"It was handball. I don't know why the referee and his assistant couldn't see it, but everyone else could. "We should have won that game. We should have put it beyond QPR with the 15-minute spell we had after half-time.
"It was a good performance but this is the FA Cup and what matters most is getting to the next round."
QPR: Royce, Kanyuka, Stewart, Mancienne, Bignot, Ward (Baidoo 72), Lomas (Bircham 72), Smith, Cook, Ray Jones (Furlong 64), Blackstock.
Subs Not Used: Cole, Rehman.
Goals: Blackstock 32, Baidoo 76.
Luton: Beresford, Barnett, Perrett, Coyne, Davis, Brkovic, Robinson, Langley, Morgan, Vine, Feeney.
Subs Not Used: Brill, O'Leary, Boyd, Keane, Holmes.
Booked: Barnett, Robinson, Langley.
Goals: Vine 45, Feeney 46.
Att: 10,064
Ref: A Bates (Staffordshire).