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ARLINGTON, Texas -- Most pitchers dread a trip to Rangers Ballpark. Not Kansas City's Zack Greinke. He kept posting zeros.

Greinke did not allow a run for his third straight start this season, pitching a seven-hitter for his first career shutout as the Royals beat the Texas Rangers 2-0 Saturday night.

The Rangers averaged nine runs in the first four games of the current homestand and were batting .350 as a team in their previous three games. But they couldn't get much going against Greinke, who's thrown 34 consecutive scoreless innings, 20 over his three outings this year.

"I just heard about it," Greinke said of the shutout streak. "It kind of blew me away. I think it's almost impossible to do 34 scoreless innings in these days. I would have taken the 20 as a career high."

Greinke (3-0) prevailed in a matchup of aces who started the day with the two lowest ERAs in the AL -- Greinke at 0.00 and Texas' Kevin Millwood at 0.64.

"You figure you give up two runs in this ballpark with this offense, it's a win," Rangers manager Ron Washington said.

Greinke struck out a season-high 10 and didn't issue a walk while getting his fourth career complete game in 106 starts. He used a variety of pitches to keep the Rangers off-balance, including a fastball in the mid-90s and an effective changeup.

"A lot of my pitches were working," said Greinke, who has a 2.00 ERA in 27 career innings at Rangers Ballpark. "My pitches were all complementing each other. Usually I don't have the slow curve working like I did tonight."

With a runner on third in the ninth, Greinke struck out Chris Davis looking to end the game, wrapping up the second shutout in the AL this year.

"I've got to swing at that [pitch]," Davis said. "It was too close to take. My performance tonight was pathetic. It was ridiculous."

Millwood (1-1) also turned in a strong effort, allowing two runs and five hits in nine innings for his 18th career complete game. He struck out three and walked three.

"It was tough. It was one of those nights," Millwood said. "You've just got to tip your hat to him."

Kansas City has won five of six. Texas has lost seven of eight.

The Royals took the lead in the sixth on Billy Butler's two-out RBI double. Miguel Olivo's two-out solo homer in the seventh extended Kansas City's lead to 2-0.

The Royals loaded the bases with one out in the second but Millwood retired Olivo on a fly ball to straighaway center field and got Willie Bloomquist on a grounder.

Greinke escaped a jam of his own in the second, allowing a leadoff triple to Hank Blalock before retiring the next three batters including strikeouts of Nelson Cruz and Davis.

Texas put a runner on third with one out in the third, but Greinke struck out Ian Kinsler and set down Michael Young on a grounder.

With a runner on first in the fifth, Millwood made a barehanded stop of Bloomquist's hard grounder and threw a one-hopper to second for the forceout. Manager Ron Washington and team trainer Jamie Reed ran to the mound to check on Millwood, who threw a couple of warmups pitches before waving Washington and Reed back to the dugout.

Millwood said the ball lodged between his index finger and thumb and that the fingers on his right hand went numb for a little while, accounting for the one-hop throw to second.

Game notes

Earlier Saturday, the Rangers purchased the contract of LHP Derek Holland, their top pitching prospect, from Triple-A Oklahoma. Texas also designated RHP Josh Rupe for assignment. The Rangers see Holland's future as a starter but he'll begin his major league career in long relief. Texas relievers have an 8.63 ERA. ...Young had his 5,000th career at bat in the first, becoming the fourth player in team history to reach the milestone. ...Olivo broke a 1-for-19 slide with his homer. ...Texas had multiple homers in its first seven home games this season, matching its longest such spell in Rangers Ballpark history, before the streak ended on Saturday night. ...The condition of Royals RF Jose Guillen, who went on the DL April 10 due to a partially torn right hip flexor muscle, has improved enough that he could be ready for an injury-rehab assignment. Manager Trey Hillman said he wasn't sure whether Guillen would go to the minors or continue to rehab without playing in games.