Watsonians used Edinburgh centre Chris Dean for the second half and he and fellow replacement Rory Drummond shifted the game for the visitors, each scoring a brace of tries.
For their part Hawick can take much from their first half-performance but a propensity to falter in defence continued to haunt them.
Two penalty goals by Ali Weir and his conversion of a try by Dom Buckley to a penalty goal by Andrew Chalmers gave Hawick a 13-3 interval advantage but the contributions of Dean and Drummond together with a try by flanker James Miller quickly changed the game.
A Keith Davies try stemmed the Watsonians flow before Dean raced in for a second touchdown. Teenager Lewis Ferguson bagged a third try for Hawick but in stoppage time Chalmers scored a try and his fourth conversion.