Edwin Encarnacion singled home the go-ahead run in the 11th inning as the Indians edged the Rangers 9-8 in Arlington.
Jason Kipnis and Jose Ramirez homered for the Tribe.
Ramirez now has a career-high and league leading 30 long balls.
Zach McAllister picked up the win and Dan Otero locked down the save as Cleveland won for the third time in four games.
Robinson Chirinos and Joey Gallo homered off Indians' closer Cody Allen in the ninth to force extra innings for Texas.