A goal in each half ensured AFC Bournemouth returned to Dorstet with all three points as Rovers suffered defeat on home turf.
Philip Billing thundered home just before the half hour mark to put the play-off chasers in front with their first foray forward.
That was all that separated the sides at the interval, with Arnaut Danjuma putting the game beyond Rovers' reach with 15 minutes remaining.
Rovers were awarded a lifeline in the form of a penalty in the dying embers of the game, but the returning Adam Armstrong saw his spot kick saved by Asmir Begovic's legs.
Armstrong was one of four changes made by Tony Mowbray, with the other alterations coming in the form of Ryan Nyambe, Bradley Johnson and Tyrhys Dolan.
Injury kept Joe Rankin-Costello out of the matchday squad, whilst Lewis Holtby, Sam Gallagher and Ben Brereton all dropped to the bench.
In an even start, it was the hosts who had the first attempt, but Harvey Elliott, a day after turning 18, saw his curled effort fly just past Begovic's right-hand post with 13 minutes played at a bitterly cold Ewood Park.
However, despite Rovers looking comfortable, the Cherries took the lead with their first venture forward just before the half hour mark.
After Danjuma's dancing feet worked a yard, the Dutchman's strike was blocked, but it fell kindly to the lurking Billing, who swept home first time to put Jonathan Woodgate's charges ahead.
Rovers responded well though and Holtby, who came on for Joe Rothwell earlier in the game, saw his glancing header held by Begovic.
Elliott went closer to an equaliser with five minutes to go until the break, but Begovic was equal to his curling attempt to fly to his right and beat away the shot.
Billing's precise strike ensured the visitors went in with the slender advantage in a half of very few changes for either side.
Armstrong went in search of changing that 10 minutes into the second-half, but his free kick drifted over Begovic's upright.
Armstrong went closer after the hour, but his lashed volley, which looked destined to find the back of the net, took the slightest of deflections off Steve Cook and went inches past Begovic's right-hand post.
Any hopes Rovers did have to take anything from the game vanished when Bournemouth made it 2-0 with 15 minutes remaining.
Like he did on the opening day of the season, Danjuma found a way past Thomas Kaminski, with the winger finding the ball int he box before slotting into the bottom corner.
Danjuma could have bagged his second and his side's third soon after, but the Dutch international dragged wide of the target after being played in by substitute Sam Surridge.
However, there was to be the offer of a lifeline in added time when substitute Gallagher was taken down in the box by Adam Smith.
Armstrong stepped up, went down the middle, but was denied by the legs of Begovic before Johnson's shot was then hacked off the line by a visiting defender just seconds later.
That was to be the last chance for Rovers to stage a late comeback, with the Cherries returning to Dorset with all three points.
Rovers: Kaminski, Nyambe (Bennett, 79), Lenihan (c), Harwood-Bellis, Douglas, Trybull (Downing, 79), Johnson, Rothwell (Holtby, 24), Dolan (Gallagher, 56), Elliott (Buckley, 79), Armstrong.
Unused substitutes: Pears, Davenport, Brereton, Branthwaite.
Booked: Elliott, 78.
AFC Bournemouth: Begovic, Smith, Carter-Vickers, S. Cook (c), Kelly, Pearson, Lerma, Brooks (Stacey, 70), Billing, Danjuma (Rico, 89), Solanke (Surridge, 83).
Unused substitutes: Travers, Mepham, Wilshere, Long, Riquelme, Anthony.
Goal: Billing, 29, Danjuma, 75.
Booked: Lerma, 50, Solanke, 51.
Referee: Darren Bond.
Virtual Match Sponsor: