Second-half goals from Coby Rowe and David Ajiboye seal all three points for the home side after Rovers missed a glorious chance to open the scoring at the start of the second half.
George Miller should have ended a goal drought which now stretches 13 games when James Maxwell put the ball on a plate for him seconds after the restart but the striker saw his effort blocked.
Moments later Sutton were ahead through Rowe before Caolan Lavery missed a great chance to equalise following his introduction.
The hosts doubled their lead through Ajiboye on the counter-attack late on.
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