Vaughan, who additionally opened the batting and scored 44 runs within the first innings, had figures of 11-140 for the match. He had earlier taken 6-102 in Surrey’s first-innings whole of 321.
England left-arm spinner Jack Leach additionally contributed considerably, taking 5-37 in 37 overs.
Surrey’s middle-order collapse from 95-3, dropping their final seven wickets for simply 14 runs, was essential, with Vaughan dismissing Bangladesh star Shakib Al Hasan for a duck.
The victory moved Somerset to simply eight factors behind First Division leaders Surrey, who’re aiming for his or her third consecutive title, with two video games remaining.