Jermaine Easter nodded Rovers ahead from Lee Brown's cross before Ollie Clarke doubled the lead with a low right-footed shot.
Jon Meades' header gave Wimbledon hope but Matt Taylor's 12-yard finish, his 19th of the season, sealed victory.
Wimbledon, who are seventh, had substitute Adebayo Akinfenwa sent off for dissent.
Fifth-placed Rovers are six points off an automatic promotion spot with 11 games to go.
AFC Wimbledon manager Neal Ardley told BBC Radio London:
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"When you assess it afterwards it's not just the points you haven't gained, it's injuries and now suspensions."
"As far as the actual game goes, I thought we were really good. They were ruthless with their chances, we made some silly defensive errors at certain times and they punished us."
"I can't ask for any more. I thought in the second half particularly we ran all over them."
Bristol Rovers strengthened their promotion hopes with victory over AFC Wimbledon, their third in a row.