ANAHEIM -- In the middle of his third full major-league season, right-hander Matt Shoemaker attained a pivotal career achievement that extended beyond statistics.

Shoemaker pitched a six-hit shutout to lead the Los Angeles Angels to a 1-0 victory over the Chicago White Sox on Saturday night in front of 39,620 at Angel Stadium.

Shoemaker (5-9) also amassed a career-high 13 strikeouts while issuing no walks in recording the first shutout of his career and his second consecutive win.

"'Shoe' had to pitch with his back against the wall against a team that has guys who can hit one mistake and tie the game," Los Angeles manager Mike Scioscia said. "It was just an exceptional effort, especially when he was getting a little tired at the end. But we felt he had enough to get through it. He still had his good splitter working and his velocity was fine."

Despite getting two hits apiece from Jose Abreu, Adam Eaton and Melky Cabrera, the White Sox have now played 32 consecutive innings without scoring.

"You're wearing if it's one game, let alone three," Chicago manager Robin Ventura said about the pressure accompanying that scoreless streak. "It's surprising in the big leagues when it goes this long. We've got to figure it out. But we'll get there."

Right-hander James Shields (2-4) retired 16 of the final 18 batters he faced, permitted only one hit after the first inning, allowed only two hits and two walks and collected two strikeouts yet lost his second successive decision.

But Shoemaker had to survive a dramatic ninth inning, when the White Sox put the potential lead run on base. Eaton began the inning by lining Shoemaker's first pitch into left field for a double.

"Matty has talked about trying to get over that hump, trying to get those outs late in the game," Scioscia said. "Tonight, he did. As that inning kept going, he kept making quality pitches."

Abreu grounded out but Cabrera followed with a single that sent Eaton to third. However, Shoemaker struck out Todd Frazier and Justin Morneau to end the game. The right-hander threw 115 pitches, one less than his season high.

"I appreciate the trust he had in me in that situation," Shoemaker said about Scioscia. "That game was a lot of fun. That ninth inning, with the crowd getting into it like it did, was awesome. That's memorable."

The Angels scored the only run in the first inning. Yunel Escobar began by hitting a triple off the wall in right-center field. Then after Kole Calhoun walked, Escobar came home when Mike Trout grounded out. Calhoun took second base on the play but catcher Dioner Navarro picked Calhoun off for the third out following Albert Pujols' groundout.

"There aren't many times when the lead-off hitter decides the game," Shields said. "But this is a crazy game. I've seen a lot of crazy stuff happen."

The White Sox put the potential tying run on second base with one out in the fourth when Abreu hit his second double of the game. But Cabrera flew out and Frazier looked at a 93 mph fastball at the knees for a called third strike.

Chicago followed suit in the sixth. Eaton just beat shortstop Andrelton Simmons' throw on a slow roller for an infield single with two out, then stole his 11th base. But Abreu struck out when he missed an 86 mph change-up.

NOTES: Chicago has hit 26 home runs in their past 20 games since June 21. ... White Sox CF Adam Eaton recorded his 500th career hit Friday night with a double in the first inning. ... White Sox LHP Chris Sale became the fifth pitcher in team history to start an All-Star Game. Sale joined Billy Pierce (1953, 1955, 1956), Early Wynn (1959), Esteban Loaiza (2003) and Mark Buehrle (2005). ... Los Angeles is batting .352 (45-for-128) with runners in scoring position and .300 (117-for-390) overall while scoring 77 runs since July 1. ... Angels DH Albert Pujols has driven home 17 runs in his past 20 games. ... Angels CF Mike Trout entered the All-Star break with 58 walks and a .425 on-base percentage, his highest first-half totals of his career. ... The Angels are wearing replicas of their 1970s uniforms this weekend.