The Giants' top pitching prospect posted career bests with 12 strikeouts over seven innings as Class A Advanced San Jose blanked the Stockton Ports, 2-0.
It was the Minor League-leading ninth shutout in 50 games for the two-time defending California League champions.
Wheeler (4-2) had surrendered seven earned runs over his previous 9 2/3 innings. But he turned things around and helped the Giants extend their winning streak to 10 games.
The sixth overall pick in the 2009 Draft worked with runners on base in five of seven innings, but he also retired nine straight batters at one point, typically leaning on the strikeout.
Wheeler ranks third in the league with 62 punchouts over 48 2/3 innings. His best previous performance was six innings of two-hit ball on May 18, 2010, when he struck out seven for Class A Augusta.
Jake Dunning and Ari Ronick worked the final two innings, with Ronick earning his first career save.
Chris Dominguez singled in a run and Tommy Joseph plated the other with a sacrifice fly as the Giants opened an eight-game lead over second-place Stockton in the North Division.