Choo has tortured the Royals of late, batting 15-for-24 with four homers and 14 RBI in six games against Kansas City in September, as the Indians won for the second time in this four-game series that ends Sunday. Jordan Brown added two doubles, while Asdrubal Cabrera had a pair of hits and scored once.
Jeanmar Gomez (4-5) snapped his five-decision losing streak after allowing one run, six hits and four walks while fanning five in five innings.
Brayan Pena drove in the lone run for the Royals, who now sit a half-game behind Cleveland for fourth place in the AL Central. Greinke (9-14) was pummeled for a season-high 11 hits and seven runs over only 3 2/3 frames.
Pena's single in the third plated Mike Aviles to open the scoring for the Royals, but the Indians turned the game into a rout with seven unanswered runs.
Cleveland first answered with a three-run third. Luis Valbuena doubled, and Luke Carlin followed with an RBI single. Two batters later, Cabrera's base hit to center plated Carlin for a 2-1 lead. After Cabrera stole second, Choo's RBI double made it a two-run game.
The Indians tacked on four more in the fourth. Jayson Nix doubled, and Matt LaPorta doubled two batters later to score Nix easily. Valbuena followed with a single and advanced on a throw to put runners at second and third, and LaPorta scored on a wild pitch with Trevor Crowe at the plate. Crowe ended up singling to score Valbuena.
Choo finished off the scoring with an RBI single for a 7-1 lead.
Gomez pitched through the fifth without allowing another run, and four Indians relievers combined to pitch four perfect innings to finish out the win.
The Indians took the lead in the season series, 9-8...The Royals are still stuck on 4,999 franchise homers after they didn't record a long ball in this contest...Greinke fell to 2-9 on the road this season.