Kansas City Royals starting pitcher Zack Greinke walks back to the dugout after the end of the sixth inning against the Los Angeles Angels. The Angels won, 1-0, Saturday in Anaheim, Calif., handing Greinke his first loss.

Anaheim, Calif. ? Facing the stingiest pitcher in the American League this season, Joe Saunders had the game of his career.

The Los Angeles Angels’ left-hander bested Zack Greinke, tossing a five-hitter to lead the Angels to a 1-0 victory against the Kansas City Royals on Saturday night.

“You know that if you give up one or two (runs), you might lose,” Saunders said. “For me, I had to bring my A game tonight; the A-plus game, really, to beat that guy the way he’s been throwing.”

Greinke (6-1) had won his first six starts, while posting a microscopic ERA of less than half a run. He was excellent again versus Los Angeles, allowing four hits, no walks and one run in a complete game. His ERA rose to 0.51.

“(My stuff) was all right — I can’t complain — but not good enough,” said Greinke, who had three-ball counts on six of the first seven batters he faced. “It was a tough game.

“A loss is a loss. It might be a little tougher, but the end result is the same thing.”

Saunders (5-1) was even better, posting his first career shutout and second complete game. Chone Figgins’ sacrifice fly in the third inning was all the support he needed. Figgins also came up big with his glove.

Saunders had to work out of a second-and-third situation with one out in the eighth. Figgins got the second out when he tagged Miguel Olivo running from second base on a ground ball from Coco Crisp.

With David DeJesus at the plate, Figgins had to go to his right, toward the line, where he made a sliding stop of a sharp grounder. He then threw across the diamond to get DeJesus by a step and end the inning.

Saunders clapped the back of his glove and emphatically pointed at Figgins while leaving the mound. Figgins got the revenge he was seeking after DeJesus made a catch on his line drive in the first inning.

“I know he’s going to want to make a play on me,” DeJesus said. “That’s what he said to me: ‘You robbed me; I’m going to rob you.’ Hey, what can you do?”

Saunders closed out the victory by striking out Mark Teahen and Jose Guillen to open the ninth and sealed it by getting Billy Butler to fly out to center field. It was the Angels’ first shutout since Ervin Santana did it on May 5 of last year.

“Just for us to win like we did, it’s very pleasing as a player to know that you can do something like that,” Saunders said. “You know it’s in you, but you haven’t done it yet so when it finally comes out it’s very rewarding to yourself. It’s just an awesome feeling.”

The Angels scratched out a third-inning run against Greinke. Gary Matthews Jr. led off the third with a double to right field. Erick Aybar’s sacrifice bunt moved Matthews to third base, and Figgins followed with a sacrifice fly to center field.

The run snapped a 15-inning scoreless streak for Greinke. He opened the season without allowing a run through in his first four starts. He gave up just four hits to the Angels.

The Royals also missed out on a scoring chance in the fifth inning when Butler led off with a walk that was followed by Alberto Callaspo’s single.

Saunders then retired the bottom of the Royals’ lineup in order.