Cleveland tied the 2002 Oakland Athletics. The only longer streaks are 21 games by the 1935 Chicago Cubs and 26 by the 1916 New York Giants, although there was a tie game during New York's streak. The Indians have outscored their opponents 134-32 during their run.
Kluber (16-4) struck out eight and did not walk a batter.
The shutout is the Indians' seventh during their winning streak, and their major league-leading 19th for the season overall.
Detroit starter Matthew Boyd (5-10) threw 116 pitches in five innings but managed to hold the Indians to one run and six hits with five strikeouts and one walk.
Red Sox 11, Athletics 1
BOSTON -- Mookie Betts hit two-run homers in consecutive at-bats and drove in six runs as Boston routed Oakland.
Betts homered in the fourth off Athletics starter Sean Manaea (10-10) and in the sixth against Raul Alcantra. He also added a two-run triple off Manaea, who was tagged for seven runs on 11 hits in 3 2/3 innings.
The Red Sox's Eduardo Rodriguez (5-5) pitched six innings of one-run ball in winning for the first time since May 26. He was 0-4 in 11 starts in between.
Rays 2, Yankees 1
NEW YORK -- Adeiny Hechavarria's one-out homer in the bottom of the eighth inning snapped a tie and lifted Tampa Bay over New York at Citi Field.
It was the second contest of a three-game series relocated from Tropicana Field because of Hurricane Irma's impact on Florida's Gulf Coast.
Hechavarria, who missed hitting for a cycle by a home run Monday in the series opener, crushed a Sonny Gray offering deep into the left field seats to give the Rays their second win in six games.
Matt Holliday hit an RBI double for the Yankees.
Braves 8, Nationals 0
WASHINGTON -- Julio Teheran pitched seven innings, Freddie Freeman was 3-for-5 with a three-run homer and Atlanta blanked NL East champion Washington.
Teheran (11-11) gave up seven hits with two walks and five strikeouts while throwing 101 pitches.
Gio Gonzalez (14-7) allowed five runs on seven hits five innings.
Blue Jays 3, Orioles 2
TORONTO -- Richard Urena singled in the winning run as Toronto scored twice in the ninth inning to hand Baltimore its sixth straight loss.
The winning hit came after Luke Maile singled in the tying run against Zach Britton (2-1).
Tim Beckham hit the go-ahead home run in the eighth inning against Blue Jays starter Joe Biagini after the Orioles tied the game in the seventh on Mark Trumbo's single.
Royals 4, White Sox 3
KANSAS CITY, Mo. -- Brandon Moss hit a grand slam and Kansas City held off Chicago.
Royals starter Sam Gaviglio (4-5) allowed two runs on six singles and a double over five innings.
Yolmer Sanchez and Rob Brantly delivered RBI doubles for Chicago.