ANAHEIM, Calif. -- The fact that Yu Darvish was winless in his first two starts of the season for the first time in his major-league career had precisely nobody in the Texas Rangers organization concerned.

They understood that in one start there was a bullpen failure and in the other start there was a lack of offense. So, on Thursday afternoon at Angel Stadium, Rangers manager Jeff Banister had a message for his ace right-hander.

Just be Yu.

Darvish struck out 10 while shutting out the Los Angeles Angels on five hits over seven innings, lifting the Rangers to an 8-3 victory.

"This is exactly what Yu needs to do when he goes out there," Banister said. "He's got to pound the strike zone because he's got swing-and-miss stuff. He's got to get ahead, and he got ahead early today. He didn't have a lot of 0-2 counts but was able to get enough with the swing-and-miss. And I think the up and down game with the fastball played well for him."

Darvish mixed his pitches well and kept the Angels hitters off balance all afternoon. He struck out two batters in each of the second, third, fourth and fifth innings, and retired the side in order in the fourth and seventh frames.

The Angels' best chance to score against him came in the sixth, when singles by Mike Trout and Andrelton Simmons put runners on first and third with one out. But Darvish, who made 103 pitches in all, induced a 4-6-3 double-play grounder from Cameron Maybin to end the threat.

Darvish uncharacteristically showed some emotion with a fist pump after getting through the inning.

"This was a situation in the games before when we struggled," Darvish said through an interpreter. "Those situations we need to get a zero on the scoreboard. That makes a big difference later in the game. I wanted to put a zero up in that situation to keep the good momentum going."

The Rangers spread the wealth offensively as all but one hitter in the starting lineup had at least one of the club's 11 hits. Backup catcher Robinson Chirinos made the most of his opportunity, getting two hits, driving in three and scoring twice.

Carlos Gomez and Nomar Mazara each homered for Texas, which won two of three in the series.

Angels starter Ricky Nolasco was on the wrong end of most of those hits. He was finished after five innings, making 97 pitches and giving up five runs and eight hits. He struck out seven and walked none.

"He just didn't have the same crisp command that we know he has when he's really on," Angels manager Mike Scioscia said. "He gave a lot of counts away and had trouble getting the ball into the zones he wanted to, and some of the mistakes he made were hit pretty hard. He's got to get back to basics, and he will. It just was a day he didn't have that good command like he usually does."

The Rangers got to Nolasco early, with Gomez hitting Nolasco's second pitch of the day over the fence in center field for a leadoff homer.

In the second inning, the Rangers got a couple two-out RBI hits -- a double by Chirinos and a single by Jurickson Profar, giving Darvish and the Rangers a 3-0 lead.

Mazara's two-run homer in the third inning, his third of the season, widened the Rangers' lead to 5-0.

The Rangers made it 8-0 in the sixth with three more runs, getting a two-run single from Chirinos and an RBI single from Shin-Soo Choo off Angels reliever Daniel Wright.

Danny Espinosa's three-run homer with two outs in the ninth inning accounted for the Angels' only runs, much too little too late because of the way Darvish pitched.

"We had some early looks at him, but we left some runners on base," Scioscia said. "That could have maybe changed the game as we went on, but he finished strong, got better as the game went on. We didn't get too many good looks against him after the first couple innings."

NOTES: Angels LHP J.C. Ramirez will start Friday against Kansas City, taking the spot in the rotation from injured RHP Garrett Richards (strained biceps muscle). Ramirez, in his fourth major league season, has pitched in 111 career games, but none as a starter. ... Because of off-days, the Rangers had not needed a fifth starter until this Saturday's game against the Mariners. RHP Andrew Cashner is the "frontrunner" to make the start, according to Rangers manager Jeff Banister. RHP Nick Martinez is another option.