Clevinger also tossed 10 strikeouts in five shutout innings in New York. He is now 8-2 on the season.
"Even with the punch-outs, those weren't easy at-bats," Clevinger told reporters. "I think maybe two of them were less than four pitches. Even when I was getting up in counts, they were making me throw four, six-seven pitches."
The Indians used a four-run second inning to take control of the contest. Greg Allen reached base on a fielder's choice, allowing Franmil Reyes to score the game's first run. Indians slugger Mike Freeman followed with a three-run homer in the same inning for a 4-0 advantage.
Indians star Francisco Lindor added to the lead with his 21st homer of the season in the fourth frame. Oscar Mercado plated Freeman with an RBI single in the sixth inning for a 6-0 edge.
The Yankees responded with a D.J. LeMahieu two-run homer in the bottom of the seventh inning. Mercado returned to the plate in the top of the next inning and hit a two-run homer, giving Cleveland an 8-2 advantage.
LeMahieu plated Gleyber Torres on an RBI single in the bottom of the ninth inning. Aaron Judge continued the rally with an RBI double in the next at-bat, but the Yankees could not complete the comeback.
Yankees pitcher CC Sabathia allowed four hits and four runs in three innings. Sabathia took his seventh loss of the season due to the short outing.
Mercado was 3-for-4 with three RBIs, a run scored and a walk in the win. Freeman was 3-for-4 with three RBIs, three runs scored and a strikeout for the Indians. LeMahieu was 2-for-5 with three RBIs, two strikeouts and a run scored out of the leadoff spot for the Indians.
The Indians face the New York Mets at 7:10 p.m. EDT Tuesday at Citi Field in Queens. The Yankees battle the Oakland Athletics at 10:07 p.m. EDT Tuesday at RingCentral Coliseum in Oakland, Calif.