Trout's solo drive off Yusmeiro Petit (1-1) in the eighth helped the Angels stop a three-game skid.
It was the 20th multi-homer game of Trout's career, which tied Tim Salmon and Vladimir Guerrero for the franchise record.
Los Angeles trailed 9-4 in the fourth when Trout began the rally with a two-run drive into the Angels' bullpen in left field.
Chapman gave Oakland a 5-3 lead an inning later with a two-run drive to center for the fifth multi-homer game of his career.
He will be opposed by right-hander Dylan Bundy (2-1, 2.08), who threw the Angels' first complete game since 2018 last Wednesday at Seattle.