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ARLINGTON, Texas -- After all those solo home runs, Nelson Cruz and the Texas Rangers got a few extra runs with their big swings.

They might finally be finding their offensive groove.

Cruz hit his fifth career grand slam, one of four homers by the Rangers in an 11-3 victory Sunday to complete a three-game sweep over the Seattle Mariners.

"It's good to have that kind of momentum," Cruz said.

Leonys Martin's first major league homer tied the game 1-all in the third, the first of four consecutive innings that Texas homered. That was the 19th homer of the season for Texas, the 15th solo shot, but the rest Sunday produced multiple runs.

Mitch Moreland hit a two-run homer in the fourth, followed by Cruz's slam that went an estimated 431 feet to left-center field that capped a five-run fifth that chased Aaron Harang (0-2). Adrian Beltre hit a two-run homer in the sixth. It was the third homer this season for each of them, Beltre's snapping a 1-for-13 slide and Moreland's a 1-for-20.

"It looked like the first couple of innings we were having problems just trying to figure Harang out," manager Ron Washington said. "Then Martin got us on the board. After that, pitch count started rising a little bit and he made some mistakes and we capitalized. It was nice to have that breakout."

The Rangers set their season high for runs in a game and scored 23 times in the series. In the series-opening 7-0 victory, they matched what had been their season high and had a six-run inning that doubled their previous highest-scoring frame.

"We definitely took a step forward for sure with the runs we put up over the three games," Moreland said. "If we can keep doing that, and keep taking care of business, and our pitching keeps throwing like they are, I think we'll be all right."

The Rangers (12-6) overtook Oakland by a half-game for the AL West lead by completing their first series sweep since last June. Texas had lost seven consecutive series finales with a chance for a sweep since winning all three games at San Diego.

Justin Grimm (1-0) struck out nine and walked one over six innings in his fourth major league start, the second this season. The right-hander allowed two runs, including an unearned run in the first that snapped the Mariners' 19-inning scoreless streak after they were shut out the first two games of the series.

Michael Kirkman pitched the final three innings for his first career save.

Grimm made his second start in place of All-Star left-hander Matt Harrison, the Opening Day starter who will have surgery Tuesday for a herniated disc in his back and be out of rotation until likely after the All-Star break.

Harang had last pitched at Rangers Ballpark 10 seasons ago, yet the results weren't any better a decade later allowing eight runs and eight hits in 4 2/3 innings. He struck out five and walked two.

"I think the last time I pitched here, the same thing happened," Harang said. "It's one of those parks, you've got a notch up on your belt that the outcome hasn't been good. Hopefully later in the year, once we come back down here, things will be different."

In three starts at Texas for Oakland, the last on June 25, 2003, Harang had a 12.34 ERA. That figure went up to 13.22 (allowing 24 runs in 16 1/3 innings) in what was surprisingly his first loss in that stretch.

Seattle snapped its scoreless streak only two batters into Sunday's game.

Endy Chavez reached on an error leading off, getting to second base when his ground rolled off second baseman Ian Kinsler and trickled into shallow right-center field. Kyle Seager followed with his majors-leading 10th double that stretched his hitting streak to 10 games and made it 1-0. Chavez had an RBI double in the fifth, and Seager hit a solo homer in the ninth.

Seattle hitters had 11 more strikeouts, giving them 32 in the series and 63 in five games.

"I'm just upset, to say the least, to our approach with two strikes, it's something that's been addressed, something that has to be better," manager Eric Wedge said. "The strikeouts are ridiculous. ... We kind of crashed as a team offensively."

Game notes

Felix Hernandez (1-2, 2.20 ERA), whose win came on opening day, is set to start Monday when the Mariners play at Houston for the first time since 2007. ... Texas opens a three-game series at the Los Angeles Angels on Monday night with Derek Holland (1-1, 1.64) on the mound. ... Seattle has never been shut out three consecutive games. ... The Rangers said fans this weekend donated tens of thousands of essential items and $40,000 in cash donations for relief efforts in West Texas, following the fertilizer plant explosion there Wednesday night. There were 80 donors during a blood drive Sunday at Rangers Ballpark.