ARLINGTON, Texas -- The Texas Rangers have found their stride and in doing so may have put a halt to the faint hopes of the Kansas City Royals repeating as World Series champs.

Mitch Moreland homered for the fourth time of the four-game series as the Rangers completed a sweep of the Royals with a 5-3 win on Sunday.

The Rangers moved six games ahead of Houston in the American League West with the win, their largest lead since July 9. Kansas City has now dropped eight of its last nine games. The Royals won just seven times in July, matching a club record for the fewest wins in the month.

Moreland's two-run homer in the fourth off Dillon Gee (3-5) gave the Rangers a 4-1 lead and enough cushion for Lucas Harrell (3-2) and the Texas bullpen to get the job done.

The Rangers got three quality starts in the series and their rotation had a 2.70 ERA to go along with timely hitting.

"It was definitely a big series for us," Moreland said. "It's been complete games, every game, hard-fought games. It starts with our starting pitching. They've done a great job keeping us in ballgames and keeping it close and really battling out there and giving us a chance as an offense to put some runs on the board and help win the ballgame."

Harrell, who was acquired from Atlanta Wednesday, gave up three runs on four hits in six innings of work in his Texas debut. The Rangers used four pitchers in relief of Harrell, with Sam Dyson working the ninth for his 22nd save as the Royals were held to four hits.

Kansas City trailed 4-1 in the fifth before rallying for two runs. Catcher Drew Butera opened with a homer off Harrell and Alcides Escobar delivered a one-out RBI single to make it 4-3.

But Harrell retired the final two batters of the fifth and worked a perfect sixth before Texas went to the bullpen.

"I'm not a savior," said Harrell, who won for the first time in his career at Globe Life Park. "I'm not anything like that. I'm another guy out there trying to help the team win. The pressure I put on myself is to help this team win."

Kansas City's offense did little to help Gee. The Royals didn't have a hit after the Escobar single in the fifth Texas pitchers retired the final 11 batters.

"Times are just rough," said first baseman Eric Hosmer, who gave the Royals a brief 1-0 lead with a homer in the top of the first. "We've got to continue to grind through it, try to find a way. Everyone's doing what they need to do to try to win. It's just not happening."

Gee, who played collegiately in Arlington, was charged with four runs on seven hits in his six innings. He struck out two.

The Rangers countered the Hosmer homer with two runs in the bottom of the first on two-run shot to right from rookie Nomar Mazara.

Gee was working from behind from then on.

"I felt like I pitched pretty well today," Gee said. "I made a couple mistakes that they obviously capitalized on."

Texas added an insurance run in the seventh inning on an RBI double from Hanser Alberto.

Moreland and Delino DeShields each had two hit for Texas.

NOTES: Kansas City put RHP Wade Davis on the 15-day disabled list with a flexor strain in his right elbow. The move is retroactive to July 27. The Royals called up LHP Matt Strahm from Double-A Northwest Arkansas to take Davis' spot. ... Texas OF Shin-Soo Choo will take batting practice with the Rangers Tuesday in Baltimore and hopes to be activated from the disabled list Thursday. Choo has been out since July 20 with lower back inflammation. ...RHP Lucas Harrell became the 11th starter used by the Rangers this season Sunday. That's tied for the most in the American League and one shy of the total starters used by Texas in 2015. ...The home run Brooks Pounders gave up Saturday night was the 140th allowed by the Royals this season, the second highest total in the majors. Kansas City pitchers allowed 155 the entire 2015 season.