Yonder Alonso and Rajai Davis homered in the fifth inning while Matt Joyce doubled, scored and drove in a run to help the A’s beat the Indians in the opener of the series after dropping three of four in Cleveland earlier this season.
It is the third shutout by Oakland this season.
Gray (5-4) allowed two hits over six innings with five strikeouts and one walk in one of his strongest outings this season. Both of the hits came in the third inning, one an infield hit by Erik Gonzalez.
Three relievers combined for the final nine outs. Santiago Casilla retired three for his 16th save.
Francona returned to the Indians bench following a six-game absence when he underwent a minor procedure for an irregular heart beat last week.
The Cleveland skipper had also been tabbed to manage the American League in Tuesday’s All-Star Game but had to opt out.