QPR lost a two-goal lead in an all-too familiar early exit from the FA Cup.
Championship strugglers Rangers scored twice in the space of as many minutes shortly before half-time, with Sinclair Armstrong putting them ahead and Lyndon Dykes doubling their lead.
But Marcus Tavernier pulled a goal back three minutes into the second half, Keiffer Moore equalised 10 minutes later, and Justin Kluivert’s winner took the Premier League side through.
Armstrong’s 40th-minute opener was a beauty. The young striker collected Ziyad Larkeche’s ball down on the left, breezed past Marcos Senesi and superbly lifted the ball over keeper Mark Travers.
Dykes’ goal came from a similar position. He found space on the left and saw his shot strike Cherries defender Max Aarons and loop over Travers.
Alex Scott missed a golden chance to pull a goal back before the interval when he shot woefully over while unmarked.
Bournemouth did find the net soon after the restart and this time benefited from a deflection.
A cleverly-worked corner routine saw Scott deliver to the near post and Philip Biling flick the ball towards Tavernier, whose shot hit R’s defender Jimmy Dunne, wrong-footing Asmir Begovic.
Keeper Begovic, playing against his former club, produced a fine double save to temporarily prevent an equaliser, denying first Luis Sinisterra and then Tavernier.
However, from Scott’s resulting corner, Moore headed home to haul Bournemouth level as QPR yet again conceded from a set-piece.
Rangers have let in 14 goals in their 13 matches since Marti Cifuentes took over as boss, with nine of them coming from set-pieces.
And the Bournemouth winner on 69 minutes also came as a result of dismal defending by Cifuentes’ side, this time as they attempted to play the ball out from the back.
Billing robbed Jimmy Dunne, who insisted he was fouled, and teed up Kluivert for a simple tap-in from three yards out.
The result continued QPR’s wretched FA Cup record – they have now gone out in the third round in 15 of the past 20 seasons.
Staying in the Championship is their immediate concern though, and they have little chance of avoiding the drop unless their defending improves.
After managing to quell Armstrong, who caused them major problems in the first half, Bournemouth were deserved winners and their second-half onslaught was simply too much for their opponents to handle.
Tavernier almost added a stoppage-time fourth with a mis-hit free-kick which clipped the top of the bar.
QPR: Begovic, Drewe (Kakay 61), Dunne, Fox, Larkeche, Field (Talla 80), Dozzell, Dixon-Bonner (Pedder 81), Smyth (Adomah 61), Armstrong, Dykes (Paal 80).
Subs not used: Salamon, Clarke-Salter, Cannon, Duke-McKenna.