The Hornets, who made a host of changes but should still have boasted a team strong enough to advance, paid the price for making a sluggish start in both halves as Rovers scored early in both periods.
Paul Dickov’s men started brightly and James Coppinger and Nathan Tyson went close before the visitors were rewarded for their early efforts in the 12th minute.
When Gabriel Tamas tripped Kyle Bennett in the penalty area, Tyson fired emphatically past goalkeeper Jonathan Bond from 12 yards.
Lewis McGugan rattled the crossbar from 25 yards as the Hornets sought an instant reply and they were to get back on level terms in the 31st minute.
A smart flick from Odion Ighalo released Lloyd Dyer and, after running at the Doncaster defence, he powered a shot beyond Jed Steer.
Rovers were quicker out of the blocks after the restart and they regained the lead in the 51st minute when some fine work by Dean Furman allowed him to lay the ball inside the area for Liam Wakefield to convert from eight yards.