Second-half goals from ex-Rovers striker James Hayter and substitute Gozie Ugwu secured the home side's third consecutive League One victory.
The hosts, who were beaten by West Brom in Tuesday's Capital One Cup second round, came closest to breaking the deadlock in a first half that lacked any kind of fluency.
In-form striker Reuben Reid's header struck the crossbar, with a last-ditch tackle by Doncaster captain Rob Jones denying Hayter from converting the follow up.
Yeovil started the second half with more urgency and deservedly broke the deadlock after 55 minutes when Reid's sumptuous cross was headed home by Hayter to score his third goal of the season.
Ugwu, on loan from Reading, added a second after 84 minutes having broke free of the Doncaster defence and chipping the goalkeeper, before Billy Paynter scored a last-gasp consolation for the visitors.