ARLINGTON, Texas -- Texas starter A.J. Griffin had his good stuff working Saturday and the Cleveland Indians had no answer for it.

Griffin and three relievers combined on a seven-hit shutout as the Rangers blanked Cleveland 7-0 in the battle of American League first-place teams. Texas has won two of the first three games in the series, with both coming in shutouts.

Griffin (6-3) went six innings in his first scoreless start of the season and ended a string of 11-straight starts of allowing at least one homer, which matched a franchise high. Griffin scattered five hits, struck out six and walked just one.

Tony Barnette, Jake Diekman and Matt Bush helped Griffin complete the Rangers' fourth shutout of the season.

"We were trying to move the fastball around the zone, up and down, all around," said Griffin, who logged his first quality start since May 2. "Keeping the changeup down to get them to swing over it. I threw some of my better changeups I think today and mixed in the curveball and cutter. It was just execution of the game plan.

The Rangers, held to just one run Friday, gave Griffin plenty of support against Cleveland's Carlos Carrasco (9-7). Carrasco struggled early, giving up five runs in the first inning.

Back-to-back singles with one out and a botched fielder's choice loaded the bases for Rougned Odor, who brought in the first Texas run after first baseman Carlos Santana booted his grounder. Two batters later, Mitch Moreland unloaded the bases with a grand slam to right.

Moreland, who went just over four years between his first and second grand slams, knew it would be important to get to Carrasco early.

"It's always nice to put some runs early, especially against a good team like that, a good pitcher," said Moreland, who is now one homer shy of matching his career high of 23. "To be able to scratch a few early and set the pace, set the tone, let A.J. fall into his rhythm, it's always nice to do that."

The Indians helped plenty in the first inning. In addition to the Santana error, there was a missed chance for an out on the fielder's choice and a Carrasco balk.

"Just so many things happened in the one inning," Cleveland manager Terry Francona said. "The balk doesn't help. Then the ball to [third baseman] Jose [Ramirez] started out getting him back to third base and then thought we had a chance to get him and didn't. So we lose an out there. Then the ground ball to Carlos. It was a bad inning."

Texas wasn't done against Carrasco. In the third inning, a double and a walk put runners on for Elvis Andrus, who drilled a two-run double to left-center to push the Texas lead to 7-0.

Carrasco lasted just four innings and gave up seven runs (three earned) on eight hits. He struck out eight. To save its bullpen, Cleveland turned to catcher Chris Gimenez to pitch the eighth and he retired the side in order.

Carrasco was coming off a start in which he pitched eight scoreless innings against Oakland. He didn't have it Saturday.

"I feel completely different," he said. "I think I missed a lot of my pitches' location. That's what happened. A team like that, every pitch that I miss I get hurt. I think I have to be better than that, locate my pitches."

Texas finished with 10 hits. Andrus, Carlos Beltran and Ian Desmond each had two. Jose Ramirez had three of the seven Cleveland hits.

NOTES: Major League Baseball has decided to keep Texas Rangers pitcher Jeremy Jeffress on the suspended list. Jeffress was arrested and charged with a drunk-driving offense on Friday. There is no timetable for his return to the roster. ... Texas RHP Colby Lewis, who is rehabbing from a strained right lat, will throw 60-65 pitches in a rehab start for Double-A Frisco on Monday. ... Friday night's offensive output from Cleveland's Abraham Almonte and Roberto Perez marked just the second time in the last 40 years that the Indians have recorded at least three hits and three RBIs from their Nos. 8 and 9 hitters in the same game. ... The Indians lead the American League in steals, but entered Saturday without one in a season-high nine consecutive games.