CLEVELAND (AP) -- Yan Gomes hit a grand slam to highlight Cleveland's nine-run second inning against two Kansas City rookie left-handers as the Indians completed a three-game shutout sweep over the Royals with a 12-0 win on Sunday.
Carlos Carrasco (13-6) allowed six hits in seven innings, and the Indians, who haven't given up a run in 28 innings, outscored the Royals 20-0 in the series.
It's the first time Cleveland has posted three straight shutouts since 1956.
Kansas City hasn't scored in 34 consecutive innings, a team record and the longest drought in the majors this season.
Francisco Lindor hit a two-run homer in the second off Eric Skoglund (1-2) before Carlos Santana connected for a three-run shot against Onelki Garcia. Gomes capped Cleveland's biggest inning this season with his drive off the reliever, who was promoted from the minors Saturday and made his first major league appearance since 2013.
Carrasco followed strong starts by Ryan Merritt and Mike Clevinger in shutting down the Royals. Of course, it helped that he took the mound in the third with a 12-run lead.
The three-game dusting by the AL champions all but ended Kansas City's chances of catching Cleveland in the division. The Royals fell nine games out of first in the Central, but remain in the thick of a wide-open, wild-card chase.
The Indians showed no mercy in the second when they teed off on Skoglund and Garcia. The Royals were in a bind after placing scheduled starter Danny Duffy on the disabled list Saturday with a sore elbow.
Already down 3-0, Skoglund gave up a leadoff single before Lindor hit his 24th homer. Austin Jackson followed with a double, and Skoglund yielded a one-out walk before being pulled. Garcia came on and Santana belted his second pitch off the left-field foul pole for his 20th homer.
The Indians loaded the bases on two singles and a walk before Gomes connected for his ninth homer and second career slam.
Cleveland didn't waste any time getting to Skoglund, who hadn't pitched for the Royals since June 9 and found himself in a quick 3-0 hole.
Lindor walked and Jackson singled before Jose Ramirez, who came in batting just .130 (3 for 23) on the homestand, pulled an RBI double down the left-field line. Edwin Encarnacion followed with an RBI groundout and Brandon Guyer drove in Cleveland's third run with a two-out, run-scoring single.
Royals: An MRI taken on Duffy showed no structural damage and nothing alarming. Manager Ned Yost said his status will be re-evaluated when the team returns home.
Indians: OF Lonnie Chisenhall went 0 for 3 and played left at Double-A Akron as he nears a return from a calf injury. … OF Abraham Almonte (strained hamstring) is scheduled to play Monday at Triple-A Columbus. … RHP Danny Salazar will throw off flat ground Monday as he recovers from a stiff elbow that landed him on the disabled list.
Royals: Ian Kennedy, who hasn't beaten the Tampa Bay Rays since his major league debut for the Yankees in 2007, starts the opener of a three-game series. The right-hander is 0-4 against the Rays over the past 10 seasons. Austin Pruitt starts for Tampa.
Indians: Corey Kluber can help his Cy Young candidacy on the Yankee Stadium stage as Cleveland opens an 11-game road trip in the Bronx. Luis Severino starts for New York.