Rangers went ahead early on when Dominic Ball's close-range flick appeared to be turned into his own net by home defender Michael Morrison.
But Reading equalised in the 35th minute when midfielder John Swift cleverly guided in on the break.
Swift completed his hat-trick with cool finishes in the 64th and 77th minutes, but substitute Andre Gray made it 3-2 with 11 minutes left and skipper Stefan Johansen levelled in the first minute of stoppage time.
QPR had won three of their previous five league games this term and have also reached the third round of the Carabao Cup, in which they will play at home to Everton.
Reading had lost five of their six opening outings, including their past three in the Championship.
QPR began brightly, with Moses Odubajo seeing an early shot blocked after a poor clearance from home skipper Liam Moore.
Chris Willock then delivered a precise cross from the left, but there was no team-mate on hand to provide the finish.
Reading showed little going forward and it was no great surprise when Rangers went ahead in the 11th minute.
Johansen slung over a deep free-kick, Jordy De Wijs nodded it back from the far post and Ball appeared to nudge it on in the six-yard box.
Centre-back Morrison seemed to get the final touch, the ball eventually squirming in off a post, and was credited with an own goal.
Reading threatened only rarely but, from an isolated attack, drew level 10 minutes before the break.
Alen Halilovic chipped a fine pass to Swift, who controlled it neatly on his chest before slotting precisely past goalkeeper Seny Dieng.
It was Reading who began the second half the better, with Swift crowded out when well placed for a shot and Halilovic sending a 20-yard effort too high to trouble Dieng.
Rangers gradually reasserted their first-half superiority and went close to restoring their one-goal advantage.
A scramble in the home area allowed Charlie Austin to pounce quickly, but his fierce attempt was well saved by keeper Rafael.
Reading replied immediately with their best move of the match, a slick-passing affair that ended with them taking the lead in the 64th minute.
Swift's crisp turn and finish, after being released by Tom Dele-Bashiru, comfortably beat Dieng.
The former Chelsea player was at it again 13 minutes later, skilfully turning in an excellent cross from Baba Rahman.
QPR ensured a hectic final when Gray poked in after a melee in the home area in the 79th minute.
And,, after another melee in time added on, Johansen hammered home to salvage Rangers' unbeaten record.