Rovers turned on the style at Priestfield to record only their third competitive victory at Gillingham.
John Marquis, Mallik Wilks and Danny Andrew were on the scoresheet for Rovers, with a late goal for the home side doing nothing to take the gloss off the performance.
Rovers return to the Keepmoat Stadium to take on Rochdale on New Year's Day, tickets are available from tickets.clubdoncaster.co.uk.