Kyle Joseph opened the scoring with a superb acrobatic finish in the first half, netting his first goal since joining Boro from Hull City during the summer.
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Doncaster had started brightly, but Sol Brynn made several important saves before Middlesbrough took control.
Substitute Will Lankshear doubled the visitors’ advantage 12 minutes from time with a close-range finish, his fourth goal of the season.
Jeremy Sarmiento then added a third with an excellent chipped effort late on, while Doncaster’s stoppage-time strike proved only a consolation.
Manager Kim Hellberg made five changes from the side that drew with Blackburn Rovers, but his team eventually found their rhythm and controlled the contest.