Striker Price headed home on just 56 seconds to give his side the lead and then struck his second goal in the 71st minute to seal the game.
Bournemouth played 50 minutes of the match with 10 men after referee Andy D'Urso gave midfield Shaun Cooper his marching orders for two bookable offences.
Bournemouth almost went two down after 18 minutes when James O'Connor linked up with Price, who back-heeled the ball to Cherries old boy Brian Stock in the penalty area.
Rovers captain Stock blasted wide of the left-hand post with the goal gaping.
In a bad tempered clash, Cooper was booked in the 29th minute after he got in a pushing match with James Coppinger.
Referee D'Urso earned the anger of the Cherries fans eight minutes later when he waved away penalty appeals after it looked like Marvin Bartley was brought down in the box.
The crowd were even more furious in the 40th minute when D'Urso sent off Cooper after an ugly 15-man pushing and shoving match on the halfway line.
Rovers Price and Mark McCammon were also put in the book for their part in the incident.
Bournemouth re-organised after the break and left young target man Sam Vokes ploughing a lonely furrow up front by himself and they tried to hit Rovers on the break.
But the mood worsened as Rovers took a deserved 2-0 lead in the 70th minute.
Midfielder Richie Wellens fed a fine through ball to Price, who finished right-footed past Gareth Stewart in the Bournemouth goal and into the bottom right hand corner.
Jo Kuffour went close to grabbing a goal back for Bournemouth after Vokes teed him up, but he fired straight at Neil Sullivan in the Doncaster goal from 15 yards.
Vokes twice went close as the clock ticked down, first with a fine header that flew a yard wide and then with a right-footed shot that just cleared the right upright.
This was only Bournemouth's second loss in the last six games as they look to recover from being given a 10-point penalty for going into administration.