Bauer (10-10) won for the second time in nine starts. He replaced Salazar, who was scratched because of a virus. Bauer allowed five hits and struck out seven.
Jason Kipnis, the American League's leading hitter (.324), drove in the go-ahead run with a seventh-inning single to cap a three-run rally. Kipnis, who had struck out twice and hit into a double play in his first three at-bats, delivered off Trevor Gott (2-2).
Kaleb Cowart's RBI single in the fifth drove in the Angels' only run. Los Angeles entered the night one-half game behind Texas for the second wild-card spot in the AL.
Cody Allen worked a perfect ninth for his 27th save.