Rovers slipped to a third straight defeat, as Lewis Grabban’s goal midway through the second half proved to be the difference between the two sides.
The Bournemouth striker scored the only goal of the game on 67 minutes, firing past Paul Robinson from 25 yards, for his 15th Championship goal of the season.
Rovers enjoyed plenty of possession in the first half, but failed to truly test Lee Camp in the Bournemouth goal. At the other end, Grabban missed an excellent early opportunity to fire the visitors in front, whilst Steve Cook was denied by the woodwork just before the break.
The home side didn’t fare much better after the interval and Grabban’s goal earned the Cherries a third straight win.
Before the game, manager Gary Bowyer made two changes to the side that lost against Burnley at the weekend.
David Dunn and Adam Henley dropped to the bench, with Rudy Gestede and Todd Kane given the nod in the starting line-up.
Rovers made a bright start, camped in the Bournemouth box for the opening five minutes, but were unable to create any clear-cut chances.
Against the run of play, Bournemouth almost made the early breakthrough. A ball out of defence saw Grabben gallop through on goal, but his initial effort was well saved by Robinson and his second shot was blocked by the retreating Grant Hanley.
Rovers responded well. Craig Conway delivered a brilliant ball in, which was headed behind for a corner. Conway took it himself, but Gestede’s downward header was comfortable for Camp.
Moments later, Matt Ritchie’s low long-range strike had to be tipped round the post by Robinson at full stretch.
Ritchie tried his luck from distance again on 18 minutes, but sliced his shot well wide and straight up the other end, Jordan Rhodes’ tame strike was straight at Camp.
Ritchie registered his third effort of the half on 24 minutes, but dragged his snap-shot from 20 yards wide of the far post.
A frustrating period of play followed, as Rovers were unable to turn sustained spells of possession into openings.
Rovers felt aggrieved on 40 minutes, as Gestede’s fancy back-flick sent Varney through on goal. He looked to be dragged down by the last defender, but the referee remained unmoved.
Bournemouth ended the half strongly and came closest to opening the scoring. On 42 minutes, Ritchie’s fourth long-range strike was deflected wide and from the resultant Ian Harte corner, Cook headed onto the foot of the post.
Rovers scrambled the ball behind and from a second successive Harte corner, played to the unmarked Simon Francis 25 yards out, his crisp strike forced a fine fingertip save from Robinson.
Unchanged at the break, Rovers had the first chance of the second half, but Gestede’s volley deflected kindly into the arms of Camp.
The hosts continued to press. A Conway cross was headed well wide by Rhodes and then a Conway corner was nodded over by Michael Keane.
Rovers made a double change just past the hour mark, as Liam Feeney and Dunn came on for Varney and Gestede, but it was the visitors who broke the deadlock shortly after, as Grabban’s 25-yard shot sneaked inside Robinson’s right-hand post.
Bournemouth threatened again minutes later, but Robinson reacted well to deny Cook’s crisp strike.
Dunn looked to lead the fight-back and some neat footwork on 72 minutes sparked penalty appeals, but the referee only awarded a corner.
Another dangerous Conway cross forced Tommy Elphick to slice clear from under his own bar, but Rovers were unable to take advantage of the three consecutive corners that followed.
Rhodes headed another Conway cross over the bar on 88 minutes, as Rovers’ push for the play-offs suffered another setback.
Huddersfield away to come at the weekend.
ROVERS: Robinson, Kane, Hanley (c) (sub Williamson 75 mins), Keane, Spurr, Varney (sub Feeney 61 mins), Lowe, Evans, Conway, Gestede (sub Dunn 61 mins), Rhodes.
Subs not used: Eastwood (GK), Taylor, Dabo, Henley.
AFC BOURNEMOUTH: Camp, Francis, Cook, Elphick (c), Harte, Ritchie (sub Coulibaly 82 mins), Arter (sub MacDonald 86 mins), O'Kane, Surman, Fraser (sub Pugh 54 mins), Grabban.
Subs not used: Allsop (GK), Smith, Pitman, Rantie.
Goals: Grabban 67 mins.
Attendance: 13,081 (including 213 visiting supporters).