Trout drove a sinker from Lance McCullers Jr. over the wall in center for a two-run shot in the first inning.
The homer was a special moment for Angels manager Joe Maddon, who has coached both Trout and Salmon. Maddon was also one of Salmon's signing scouts.
"I think it's great. I'm happy to be affiliated with both guys," he said. "I know no one would be more happy for Michael than Timothy."
Trout has 14 homers this season, tied with San Diego's Fernando Tatis Jr. for the major league lead. He has four homers in the past seven games.
Trout finished 2-for-3 with three RBIs and three runs scored, including the winning run in the bottom of the 11th. He also drew three walks.
Trout, 29, is a three-time American League MVP and won the award last season. He is in his 10th season.
Trout was the 25th overall pick in the 2009 MLB draft and made his big league debut in 2011.
Salmon played his entire 14-year career with the Angels from 1992 to 2006 and was part of their only World Series championship in 2002.
The Associated Press contributed to this report.