The Tribe was already leading 4-0 when Cabrera put the game out of reach with his fourth career grand slam in the fourth inning. He he blasted the third pitch he saw from Baltimore reliever Sean Gilmartin into the left field bleachers for an eight-run Indians advantage.
Cabrera's grand slam was the ninth this season for the Indians, lifting the team's batting average to .344 (33-for-96) with the bases loaded, including 99 RBI (third in MLB). The nine slams are tied for the most in the majors with Cincinnati and Boston.
Clevinger (9-7, 3.25) allowed Baltimore's leadoff hitter to reach base in each of the first four innings and had baserunners in every inning except the fifth. But he managed to get big strikeouts when he needed them, working six shutout frames to collect his ninth win.
It's the 13th shutout by Indians pitchers this season, which is tops in the American League. Cleveland and Pittsburgh (13) trail only the Chicago Cubs (14) for the most shutouts in the majors.
Baltimore rookie Yefry Ramirez (1-5, 6.49) took the loss, allowing seven runs on seven hits and walking five. Indians center fielder Greg Allen, batting leadoff while shortstop Francisco Lindor got a day off, reached base three times against Ramirez.
Allen was hit by Ramirez's second pitch of the game and moved to second on his 11th steal of the season. Allen scored when Yandy Diaz rifled a fastball from Ramirez to the wall in right center for an RBI double.
In the second, Allen extended his hitting streak to 12 games with a two-out RBI single that plated Jason Kipnis for a 2-0 Tribe lead. The 12-game streak equals the most by a rookie in the majors this year, matching Cincinnati's Jesse Winker (July 3-21) and gave Allen his eighth RBI.
It was a solid all-around performance for Allen, who also turned in a sliding catch on a shallow pop to center by Baltimore's Chris Davis in the sixth.
Michael Brantley had two hits, including an RBI double in the fourth. Diaz added his second RBI on a bases-loaded walk ahead of Cabrera's grand slam.
Clevinger improved his record against the Orioles to 4-0, allowing one walk and scattering seven hits. He struck out seven batters and dropped his career ERA against Baltimore to 1.80, the lowest against any single opponent.
The seven strikeouts give Clevinger 155 on the year and make him the fourth Indians pitcher with at least 150. The team needed just 123 games to reach that mark, faster than 2015 (127 games) and 2016 (149).
What it means
Cleveland has won seven consecutive series and moved to 13-4 in the month of August. The Indians are 9-1 in their last 10 games and have crept to within 4 1/2 games of the No. 2 seed in the American League playoff standings.
Ramirez threw 84 pitches, 46 (55 percent) for strikes. Clevinger threw 104 pitches, 67 (64 percent) for strikes.
Thanks for coming
The Indians and Orioles drew 30,555 fans to Progressive Field on an overcast Sunday afternoon. First pitch was at 1:10 p.m. with a game-time temperature of 77 degrees and an 8 mph wind blowing in from right field.
The Indians open a seven-game road trip Monday with the first of four matchups against AL East-leading Boston at Fenway Park. Right-hander Corey Kluber (15-6, 2.68 ERA) faces the Red Sox, while righty Rick Porcello (15-5, 4.04) takes the mound for Boston.
Kluber owns a career 2-4 record and 4.45 ERA in 10 career appearances (nine starts) vs. Boston, including a 1-1 mark and 3.96 ERA in four starts at Fenway. Sportstime Ohio and WLKR-FM 95.3 will broadcast the series from Boston.