Bryan Shaw (4-3) walked Kyle Seager to start the inning before Zunino hit a 2-0 pitch into the left-field bleachers for his 17th home run.
Carlos Santana drove in two runs for Cleveland, including a go-ahead RBI single in the seventh that broke a 4-all tie.
Dustin Ackley had a two-run homer for the Mariners while Jason Kipnis hit a two-run shot for the Indians. Both home runs came in the third when the teams exchanged three-run rallies.
Ackley’s homer was his first since May 11, a span of 234 plate appearances and gave Seattle a 3-1 lead. Robinson Cano hit his 400th career double in the third, and it scored a run.
Kipnis’ homer and Santana’s sacrifice fly tied the game.
Indians starter Zach McAllister, who hasn’t won since April 21, didn’t get through the fourth. He allowed four runs and eight hits in 3 1-3 innings.
Chris Young allowed four runs in 5 1-3 innings. The 6-foot-10 right-hander dominated the Indians in his first two career appearances allowing one run in 13 innings. Young allowed one run in five innings in a 3-2 win in Seattle on June 27.