Westcott recorded his Minor League-leading 11th win after pitching a career-high eight innings Friday as the Giants shut down the Visalia Rawhide, 3-1.
The victory also gave the Giants (63-28) their third double-digit winning streak of the season and extended the Rawhide's skid to five.
After giving up Ryan LaPensee's third-inning single, Westcott (11-1) retired 12 straight batters before his defense hampered his rhythm in the seventh. First baseman Luke Anders' error preceded Alfredo Marte's RBI single and center fielder Gary Brown's own miscue.
The 25-year-old right-hander kept the Rawhide at bay, totaling three strikeouts without walking a batter.
Westcott, who went 9-3 with a 3.46 ERA across two levels last season, ranks second in the California League with a 2.91 ERA. He has gone at least seven innings in three consecutive starts but had never pitched beyond the seventh in his three-year pro career.
David Mixon struck out two of the four batters he faced in the ninth to earn his first Cal League save of the season.
Visalia starter Eric Smith was almost as tough as Westcott, limiting San Jose to one run on four hits and four walks over seven innings. He fanned three. Kevin Munson (2-3) yielded an unearned run in the eighth and took the loss.
Catcher Tommy Joseph, the Giants' No. 9 prospect, led San Jose offensively with a pair of doubles and two runs scored.