ARLINGTON – Kevin Millwood isn't the hottest pitcher in baseball, even though his ERA sits at a sparkling 1.17 after three starts and 25 terrific innings to open the 2009 season.

That distinction belongs to Kansas City right-hander Zack Greinke, and the Rangers found out Saturday night just how tough he is.

Greinke ran his scoreless-innings streak to a club-record 34 innings, dating to last season, with a complete-game, 2-0 shutout. He outpitched Millwood, who allowed only five hits in a complete game of his own.

It was just the third time in the history of Rangers Ballpark that both pitchers threw complete games.

But while Rangers hitters acknowledged how good Greinke was, they were also kicking themselves for missing two golden scoring chances that would have produced a different outcome.

"Good pitching negates good offense, bottom line," left fielder Marlon Byrd said. "The winning equation is pitching, defense and timely hitting. We didn't have the timely hitting."

The Rangers pointed to two missed opportunities – runner on third and no outs in the second inning, and runner on third and one out in the third.

Hank Blalock started the second inning with a triple to right-center field, and the Rangers had the Nos. 5, 6 and 7 hitters coming up. Byrd, though, grounded out to third, and Nelson Cruz and Chris Davis struck out.

Jarrod Saltalamacchia led off the third with a double and was sacrificed to third by Elvis Andrus. But Ian Kinsler, a player-of-the-week candidate, struck out swinging, and Michael Young grounded to second base.

Greinke (3-0) allowed seven hits and recorded 10 strikeouts. He needed only five pitches to get out of the sixth, and he ended the game by striking out Davis. Cruz had reached third during the at-bat.

Millwood was only two pitches away from matching Greinke. The Royals scored in the sixth on a two-out double by Billy Butler, who hit a sharp grounder into the left-field corner on an inside fastball Millwood wanted a bit higher.

Miguel Olivo homered in the seventh, also with two outs. Both runs came after Millwood speared a grounder with his bare hand in the fifth, but he said that play had no effect on his pitching.

"I have one job, and that's to go out and give us a chance," Millwood said. "If everybody I pitch against pitches like that guy tonight, it's either going to be frustrating or a bunch of no decisions. You've got to tip your cap sometimes."