First half goals from Jordan Rhodes, Grant Hanley and Rudy Gestede saw Rovers earn their first home win of the season.
A scintillating first half hour saw Rovers in command, Rhodes opening the scoring on 13 minutes after outmuscling Cherries defender Steve Cook to score his first of the season on his 100th appearance.
Hanley soon did likewise heading home a Tom Cairney corner, before a clever deflection from Craig Conway's shot saw Rudy Gestede notch once more.
Rovers were comfortably in control until a bizarre penalty decision against them nine minutes from time when Alex Baptiste was adjudged to have fouled Adam Smith in the box despite there appearing to be no connection. Brett Pitman converted from the spot.
That set up final ten minutes that was more nervous than it should have been, especially after Cook made it 3-2 with a 90th minute header.
Bournemouth threw goalkeeper and all into looking for an equaliser, but Rovers held out to claim a worthy win.
Boss Gary Bowyer made just the one change from the side that faced Norwich City on Tuesday.
Ben Marshall was given his first league start since January, with Lee Williamson dropping to the bench.
At Norwich in midweek Rovers should have been 3-0 up inside the first ten minutes, but on this occasion against Bournemouth they managed three goals inside 25.
After all the transfer talk surrounding Jordan Rhodes it was perhaps inevitable that he'd grab the opener, giving chase to Tom Cairney's ball over the top Rhodes robbed defender Steve Cook in the box before sliding the ball through Cherries' goalkeeper Lee Cook's legs and into the net.
It was Rhodes' first goal of the campaign, his 54th strike in 100 appearances for the club.
After Paul Robinson saved well from Junior Stanislas, Rovers increased their advantage with two goals in the space of three minutes.
The first coming on 21 minutes when Grant Hanley opened his account for the season from a Tom Cairney corner, rising highest to power home a header that Camp couldn't keep out.
A third soon followed as another Cairney corner was cleared only as far as Craig Conway, the Scot let fly from distance with Rudy Gestede deflecting it past a flat-footed Bournemouth defence and into the net.
Rovers were rampant and had further chances to stretch their lead. Rudy Gestede just nodding wide after an inviting cross from Conway, before Markus Olsson's storming run into the area saw him tee up Rhodes but he slammed the outside of the post with a left-footed effort.
The visitors were seeing plenty of the ball but it was Rovers creating all the chances, Ben Marshall almost getting in on the act as the half drew to a close but his shot was beaten away.
Inevitably the visitors came out with much more attacking intent at the start of the second half with a host of chances in the opening minutes.
Only the fingertips of Paul Robinson prevented Yann Kermogrant from reducing the scoreline on 49 minutes, the Rovers stopper flinging himself full length to tip the curling effort over the bar.
Half-time substitute Ryan Fraser fired wide at the near post before Callum Wilson was twice denied by Robinson. A crisp strike from the edge of the box was beaten away, then a shot on the angle was held at the second attempt.
Josh King replaced the hardworking Ben Marshall on the hour and immediately took the game to the Cherries. He fed Markus Olsson who fired narrowly wide, before he tried his luck himself but the shot from inside the area deflected wide.
From the resulting Tom Cairney corner kick Alex Baptiste met the ball strongly but couldn't keep his header down as it flew a yard over the bar.
Jordan Rhodes made way to rapturous applause on 77 minutes as David Dunn replaced the goalscorer however it wouldn't be a Rovers match without a controversial penalty decision and once again they were the recipients of a bad one against them.
As the visitors attacked down the right Adam Smith went over in the area theatrically after Alex Baptiste looked to have tackled the midfielder, but to the astonishment of all connected with Rovers the referee pointed to the spot.
Brett Pitman took the penalty and despatched it with aplomb high into the roof of the net as Robinson dived in the opposite direction.
Josh King wasted a glorious chance to add a fourth for Rovers with five minutes remaining, receiving a square pass from Craig Conway the Norwegian bore down on goal only to blaze his shot over the corner of the goal.
Instead it was the visitors who grabbed a second, Steve Cook heading a corner into the roof of the net to set up a nervy final few minutes at Ewood Park.
Rudy Gestede saw a goal ruled offside as the match ticked over into added time, before the officials again conspired to upset the home side by adjudging King had fouled Smith on the edge of the box.
Pitman's free kick caused a huge scramble in the area but Rovers just about cleared their lines to claim their first home win of the season.
In the end Rovers made it hard work, but you can't help feel they weren't helped by the officials.
ROVERS: Robinson, Lowe, Baptiste, Hanley (c), Olsson; Conway, Evans, Cairney, Marshall (sub King 60 mins); Rhodes, Gestede.
Subs not used: Eastwood (GK), Henley, Dunn, Varney, Williamson, Taylor.
Goals: Rhodes 13 mins, Hanley 21 mins, Gestede 24 mins,
Booked: Evans, King, Robinson.
AFC BOURNEMOUTH: Camp, Stanislas (sub Pitman 74 mins), Cook, Elphick (c), O'Kane, Daniels, Kermorgant (sub Rantie 66 mins), Wilson, Ritchie (sub Fraser 46 mins), Arter, Smith.
Subs not used: Flahavan (GK), Harte, Gosling, Cargill.
Goals: Pitman (pen) 81 mins, Cook 90 mins.
Attendance: 13,900 (including 319 visiting supporters)