Bunn was the hero for Norwich when he kept out Adel Taarabt's second-half spot-kick to earn Norwich a hard-fought point.
The draw leaves QPR rooted to the bottom of the table and stretched Norwich's winless run to eight games.
Norwich created the first opening of the game on four minutes when Robert Snodgrass beat Armand Traore down the right and picked out Wes Hoolahan inside the six-yard box, but the midfielder could only poke his shot over the crossbar.
Adel Taarabt looked the man most likely for QPR and the Moroccan went close on 10 minutes when he beat a couple of Norwich challenges on the edge of the box before fizzing his shot just wide of the target.
Shaun Wright-Phillips had QPR's final chance of a disappointing opening half when he got on the end of Taarabt's superb pass, but the winger sliced his effort well wide.
The game burst into life in the second half with Julio Cesar producing a superb save to keep out Hoolahan's close-range effort after Snodgrass picked him out unmarked inside the six-yard box.
QPR were handed a great chance to break the deadlock on 56 minutes when they were awarded a penalty after Bunn was adjudged to have brought down Mackie inside the box. Taarabt took responsibility from the spot, but Bunn, who was booked for the foul on Mackie, produced a superb save low down to his left to keep out his effort.
Taarabt was keen to make up his penalty miss and he fired a free-kick just over the crossbar before drilling in a swerving shot which Bunn did well to keep out.
QPR were piling on the pressure in search of a goal and Samba went close on 68 minutes when his header was cleared off the line by Grant Holt.
Snograss went close for Norwich on 79 minutes with a stinging 30-yard effort which Cesar was forced to turn round the post.
QPR poured forward in the closing stages in search of a breakthrough and Andros Townsend was denied by Bunn three minutes from time with the Norwich goalkeeper producing a superb save to keep out the winger's fierce effort from 25 yards.