Anderson saw his every touch booed by some fans after he appeared to make a lewd gesture to supporters following the final whistle at Tranmere Rovers on Boxing Day.
But the big defender, who captained Doncaster against the Dale, netted the winning goal in the 81st minute after Rochdale had twice come from behind to equalise.
Rovers raced into a two-goal lead inside 10 minutes thanks to Charlie Seaman’s deflected effort and Ben Close’s first goal for the club.
But the visitors quickly hit back through Devante Rodney and were gifted an equaliser when Ro-Shaun Williams put the ball into his own net while trying to clear a Cameron John cross.
Harrison Biggins restored Doncaster’s lead before the break before substitute Sinclair, whose dad Frank manages Rovers’ under-18s, hauled Rochdale level.
Anderson sent the home fans home happy when he fired home from close range following a corner.
Scroll down for our player ratings.
2. Jonathan Mitchell - 5
Little chance with the first two goals but should have done better with the third, which dipped over him. Photo: Pete Norton
3. Charlie Seaman - 8
Feels like he's caught a break with that goal. Has done well since coming into the side. Photo: Howard Roe/AHPIX LTD
4. James Maxwell - 6
Steady, if unspectacular. Nonetheless an improvement on the last game. Photo: Howard Roe/ahpix.com