The Yankees jumped ahead, 4-0, when Gary Sanchez crushed a three-run homer during the top of the first inning before the Angels chipped away at the deficit.
Angels first baseman Luis Valbuena nearly lifted a game-tying grand slam in the bottom of the first inning, but New York center fielder Hicks kept the ball in the park with a leaping grab to render the hit a one-run sacrifice fly.
Danny Espinosa drilled a two-run homer in the second inning, and in the third inning Albert Pujols scored on a wild pitch and Eric Young Jr.