Chapman and fellow rookies Jaycob Brugman and Chad Pinder knocked in three of the four runs the A's scored in the second, the only damage allowed by Yankees starter Luis Severino, who went six innings.
The Yankees worked their way back into the game against A's left-hander Sean Manaea. It started in the third inning with a three-run opposite-field homer from Northern California native Aaron Judge, his Major League-leading 23rd of the season.
The Yankees tied it in the fifth when Mason Williams singled home Ronald Torreyes, and they took the lead when Chris Carter blasted a solo home run to center in the sixth.