Darren Anderton put the Cherries ahead in the 18th minute when he broke through to tap the ball past Rovers’ goalkeeper Steve Phillips.
Craig Disley and Chris Lines missed first half chances for Rovers before Bournemouth went further in front in the 55th minute when Max Gradel caused chaos in the Rovers defence and Jo Kuffour rammed home his 12th goal of the season.
Rickie Lambert pulled a goal back two minutes later and Andy Williams, Aaron Lescott and Steve Elliot all missed easy chances for Rovers.
Bournemouth’s Danny Hollands hit the post from 25 yards and Sam Vokes missed with only Phillips to beat.
Disley struck the outside of the Bournemouth post in injury time, but the Cherries held on.