Rovers continued their unbeaten run for the season as well as booking a place in the semi-final of the Border Cup.
A hard-fought first half in which both sides had their moments failed to bring about a goal until Waverley took the lead as the interval drew near, Jason Inglis netting with a spot kick.
Three minutes later Rovers drew level when a Steven Swantston cut back was drilled home by Alan McMath.
In the second period Greg Shortreed put the home side ahead in nodding a McMath cross past Hawick keeper Kerr Brown.
Waverley then grabbed an equaliser through Declan Hogg.
Rovers, however, had the last say when Matt Scott rattled in what was to be the winner late on.