Bournemouth's hopes of avoiding relegation from League One were boosted with their fifth win in six matches, but they were hanging on desperately at the finish.
Bournemouth's chances of survival still depend on the failures of teams around them in the table.
But there were some rousing moments for a crowd of 6,867 - one of the biggest of the season at Dean Court.
It all began brightly enough for Bournemouth and they took the lead in the 18th minute when former England winger Darren Anderton strolled through a big gap in the Rovers defence before beating Steve Phillips easily.
Bournemouth went further ahead in the 55th minute when Max-Alain Gradel caused problems in the Rovers defence and Jo Kuffour drove in his 12th goal of the season.
But Rovers pulled a goal back in the 56th minute when Rickie Lambert was unmarked to score from close-range.
Both sides had further chances with Danny Hollands hitting a post from 25 yards and Sam Vokes failing with only Phillips to beat.
But the catalogue of missed opportunities came at the other end as Bournemouth wilted.Andy Williams, Aaron Lescott and Steve Elliott all missed clear openings and deep into injury time Craig Disley hit the outside of a Bournemouth post.
Rovers sent up goalkeeper Phillips for the last two corners of the match in a bid to salvage a draw, but somehow Bournemouth managed to hold on after manager Kevin Bond had brought on two defensive substitutes to bolster the back-line.
Bournemouth fell away once Anderton had limped out of the action after 64 minutes, allowing Rovers to take over the middle of the pitch where the busy Disley was outstanding.