Brantley helped the Indians get a split of the four-game series with his 12th homer of the season. He gave Cleveland its first lead of the game by lifting a 94.5 mph fastball from Chad Green (5-2) high enough to clear the right-center field fence.
The ball traveled an estimated 387 feet and Brantley needed every inch as right fielder Giancarlo Stanton scaled the fence in an ill-fated attempt to make the catch.
After Brantley's blast, Jose Ramirez singled, stole second and took third on a throwing error by catcher Kyle Higashioka. Green then hit Edwin Encarnacion on the hand, putting runners at first and third.
Encarnacion was checked out by a trainer and exited the game.
Ramirez slid in headfirst with his left hand touching the plate just ahead of Stanton's throw on a shallow fly ball by Yan Gomes to make it 4-2.
The Indians added another run when Gonzalez scored on a wild pitch by Green.
Before Brantley's first homer since June 11, Encarnacion helped the Indians overcome a 2-0 deficit by hitting a two-run homer off Masahiro Tanaka in the fourth.
Cleveland starter Trevor Bauer gave up two runs on seven hits in seven innings. Bauer pitched at least seven innings for the 11th time and received defensive help from Brantley, who made a diving catch on Walker's liner in the seventh.
Carlos Carrasco (11-5) tossed a scoreless eighth and Cody Allen tossed a scoreless ninth for his 20th save in 21 chances.
Tanaka gave up two runs on six hits in 6 1/3 innings in his second start since returning from two strained hamstrings.
The Yankees had runners at first and third with two outs in the third when Hicks slapped a single to right field for a 1-0 lead. Walker made it 2-0 by lifting Bauer's 0-1 curveball into the right-center field seats with two outs in the fourth.
Cleveland tied it with one out in the fourth when Encarnacion hammered Tanaka's first-pitch slider onto the pavilion above the high left field wall.
(This story has not been edited by Devdiscourse staff and is auto-generated from a syndicated feed.)