The Indians got two runs back when Encarnacion belted a two-run home run into the left-field seats in the top of the eighth inning, but they could get no closer than the one run deficit.
Maeda was lifted after five innings, when his pitch count hit 90, but three relievers completed the shutout to secure the right-hander's win.
Mariners center fielder Dee Gordon led off the inning with a solo home run to the seats in right field. "But it was good that (Ramirez) hit that ball early in the season, because it helps me make an impression", Suzuki said.
He homered for the second consecutive day in his best Nelson Cruz impersonation, with Cruz out with a twisted ankle suffered after his second homer in two games on Saturday. The home run to Haniger were the first two runs given up by Olson in a little over a year with the Indians.
He also had a sacrifice bunt to move Freitas over before Segura scored him and then the home run - despite having just two home runs last season with the Marlins.
Cleveland opened the scoring with Bradley Zimmer's RBI single in the second.
While Mariners manager Scott Servais said that Zunino was available in a catch-only capacity if an emergency situation cropped up that night - and it almost did with Mike Marjama getting hit on the glove hand with a bat on a catcher's interference - Zunino spent the game in the training room and clubhouse.
Atlanta's David Freitas, right, got the ball from his first major league hit from Philadelphia Phillies second baseman Cesar Hernandez on August 30.
Darvish, who joined the Cubs over the winter as a free agent, hit the first batter he faced and allowed a two-run homer to the next hitter. Cruz had an MRI on Sunday morning.
"He came down, doing the customary high-fives to everybody, everything was fine there", manager Scott Servais told reporters.