Mike Aviles followed with another hit, chasing Herrera and bringing on Tim Collins, who promptly surrendered a broken-bat double down the left field line to Kipnis, which scored Bourn with the equalizer and sent Aviles to third
Brantley followed with a run-scoring fly to right, putting the Indians ahead.
Vinnie Pestano, however, struggled to close out the win in the bottom of the ninth, allowing three hits and a walk. But he managed to hang on for his second save as Cleveland evened its three-game series.
Cody Allen earned the victory despite yielding a run in the eighth.
Eric Hosmer and Salvador Perez each drove in a run for the Royals.
2014: The Year in Music [PHOTOS]