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The 22-year-old struck out two on the way to 108 pitches over the full nine innings, recording the Angels' 12th no-hitter in franchise history.
Trout and Anthony Rendon scored three RBIs respectively, as the Angels moved to 21-11 for the season.
They hold a one-game lead over the Houston Astros at the top of the American League (AL) West, making up two of the three best records in the AL.
The New York Yankees maintained the best record in the AL, meanwhile, defeating the divisional-rival Toronto Blue Jays 6-5.
This came after Giancarlo Stanton's own three-run shot in the sixth inning, as the Yankees moved four games clear of the Rays atop the AL East with the victory.
Wood wins it for Giants
Wood allowed seven hits and struck out four in five-and-a-third innings for the Giants, who kept within touching distance of the Los Angeles Dodgers in the National League West.
Curt Casali contributed three hits and two RBIs, with the Giants claiming a fourth consecutive win to bounce back from a five-game losing stretch.