Martin Rowlands struck in injury time to earn a point for QPR in a six-goal thriller at Loftus Road.
Darren Huckerby's early strike put Norwich ahead before on-loan Chelsea midfielder Jimmy Smith and Rowlands netted to give Rangers hope.
Substitute Dion Dublin's 71st-minute effort squared the game again before Robert Earnshaw put Norwich ahead again with a late penalty.
But Rowlands then netted again from an acute angle to snatch a late QPR point.
QPR manager John Gregory:
"We gifted our three goals, which is something that was becoming a habit here.
"If everything had been perfect, they wouldn't have brought me here in the first place - but the players showed great spirit."
Norwich caretaker boss Martin Hunter on the decision to add five minutes of injury time:
"I asked the fourth official if he was counting the time on a sundial.
"The five minutes gave the home crowd a lift. But there are some proud players in that dressing room, and we showed more steel today.
"The division is very tight. No-one will run away with it this season."
QPR: Paul Jones, Lomas (Rose 90), Rehman, Stewart, Bignot, Rowlands, Bircham, Smith, Cook, Ray Jones (Gallen 77), Blackstock.
Subs Not Used: Royce, Ward, Bailey. Booked: Rehman, Smith, Lomas.
Goals: Smith 24, Rowlands 45, 90.
Norwich: Gallacher, Colin, Fleming, Shackell, Drury, Etuhu, Robinson (Dublin 67), Hughes (Safri 75), Croft (McVeigh 87), Earnshaw, Huckerby.
Subs Not Used: Camp, Ryan Jarvis.
Goals: Huckerby 4, Dublin 72, Earnshaw 84 pen.
Ref: A Marriner (W Midlands).