The German striker pounced on the rebound, after Aaron Mooy’s penalty had been saved, to end Preston’s slim hopes of making the play-offs.
The result pushes the West Yorkshire team closer to a play-off place themselves - and keeps alive their outside hopes of claiming automatic promotion.
The contest looked set to end in a draw when there was confusion deep into added time.
Jordan Hugill, who had just made it 2-2, brought down Elias Kachunga but - amid furious protests - referee Lee Probert took an age to give the penalty.
Goalkeeper Chris Maxwell was booked for time-wasting before Mooy was finally able to take the spot-kick. Maxwell dived to his left to push away the effort - only for Quaner, an 86th minute substitute, to fire home the rebound.