A mistake by Rob Dickie proved costly for QPR as they suffered their first defeat of the season.
Two down at the interval after Jaidon Anthony and Dominic Solanke netted for Bournemouth, Rangers rallied in the second half and Sam McCallum pulled a goal back, but this time they were unable to find an equaliser.
The visitors dominated early on but found themselves behind totally against the run of play after Dickie’s 12th-minute error.
The centre-back, outstanding so far this season, dithered after collecting keeper Seny Dieng’s pass and was dispossessed by Anthony, who cut in from the left and slotted into the far corner of the net.
Anthony set up the second goal, laying the ball across for Solanke to finish from close range.
Philip Billing went close to adding another Bournemouth goal in the second half when he side-footed against the post.
That let-off kept Rangers in the game – and their hopes of pulling off a second successive comeback from two goals behind were raised by McCallum’s first goal for the club.
The on-loan wing-back’s attempted cross bounced back to him off Cherries full-back Adam Smith and McCallum reacted quickly, firing past keeper Mark Travers at the near post.
Travers superbly prevented a QPR equaliser, keeping out Jordy de Wijs’ header from Ilis Chair’s corner and seconds later tipping over a header from Dickie.
And in the final seconds, Travers denied Andre Gray at point-blank range.
QPR (3-4-2-1): Dieng; Dickie, De Wijs, Barbet, Kakay (Adomah 55), Ball, Johansen, McCallum, Chair (Thomas 82), Willock; Dykes (Gray 55).
Subs: Archer, Dunne, Dozzell, Amos.