CHICAGO -- Carlos Rodon flashed brilliance at times, but he showed Tuesday night at U.S. Cellular Field just how dominant he can be for the Chicago White Sox.

The hard-throwing rookie, a left-hander, escaped a first-inning jam and used it to fuel the best outing of his career in Chicago's 3-0 victory against the Los Angeles Angels, their second in as many days.

During that key first inning, Rodon fanned Angels stars Mike Trout (0-for-4) and Albert Pujols (0-for-4) for the first two outs, with two runners on base.

"For him this is the first go-around, and he knows exactly who those guys are," White Sox manager Robin Ventura said. "I'm sure he's watched them for the last couple of years and heard about them. I thought he handled it great. From then on, I don't think there was the question of trying to feel for it. He was just letting it go."

After the first, the 22-year old Rodon made the White Sox look wise for taking him third overall in the 2014 draft. He's struggled with command issues almost all season, but his only walk against the Angels was drawn by Shane Victorino, L.A.'s first hitter of the game. Rodon filled the strike zone for the rest of his start and finished with a career-best seven innings and career high 11 strikeouts -- twice striking out Trout and Pujols.

Asked if whiffing two of the game's best hitters in the first snapped him into a good rhythm the rest of his outing, Rodon nodded.

"Yeah, you could say that," he said. "You walk the first guy and then you've got to hone in on the strike zone and just try to make pitches. I've been trying to get seven innings this whole year and it just hadn't been happening for me. So, it's good to finally get that in."

It was the second double-digit strikeout game of the season and brief career for Rodon, which made him the third White Sox rookie to accomplish that feat.

The last White Sox rookie to do it was Jason Bere in 1993. The 11 strikeouts for Rodon are the second-highest in a game for a White Sox rookie, with Bere's 12 against the Angels in 1993 the most.

Melky Cabrera, filling the designated hitter role for Chicago, led the way offensively by going 1-for-3 with a double and two RBIs. Left fielder Trayce Thompson, another Chicago rookie, added his first career homer in the fifth off Angels starter Hector Santiago.

Chicago's bullpen nearly spoiled Rodon's big night in the eighth, but right-hander Jake Petricka got out of the bases-loaded situation. Pujols hit into an inning-ending double play that was started by Petricka fielding a ball and throwing home to catcher Tyler Flowers for the second out. Flowers then threw to first for the final out.

"Actually, he made a good pitch," Pujols said. "No excuse, but I didn't really do my job. He didn't really give me anything."

Right-handed closer David Robertson closed it out in the ninth for his 23rd save.

The White Sox scored the game's first runs in the fourth, after being retired in order by Santiago through the first three innings.

Tyler Saladino got the rally started with a one-out single for Chicago's first hit before first baseman Jose Abreu was hit by pitch. Cabrera drove in Saladino and Abreu with a double, and Thompson's homer made it 3-0 an inning later.

After a few unreturned high-fives in the dugout, Thompson was mobbed in a mass of celebratory hugs and pats on the back.

Rodon took it from there. He retired the Angels in order in the sixth, including his second strikeout of Pujols to end the frame.

"It's part of the game," Pujols said. "It's stuff that happens. You think I want to get myself out? I want to come through every time, but it doesn't happen."

NOTES: White Sox OF J.B. Shuck (left hamstring strain) and UTL Emilio Bonifacio (left oblique strain) are each close to starting rehab assignments in the minor leagues. "Once they go out and start playing, we're going to get a better idea of what they can do," manager Robin Ventura said Tuesday. ... Angels manager Mike Scioscia said LHP C.J. Wilson had a scheduled meeting with Dr. Neal ElAttrache on Tuesday for a second evaluation of his injured left elbow. Scioscia said he didn't know what the recommendation was following the meeting. An earlier MRI showed Wilson has bone spurs in his elbow. ... Scioscia said the Angels are monitoring the innings of LHP Andrew Heaney, who started the season at Triple-A Salt Lake. Heaney has thrown 129 2/3 innings between Triple-A and the Angels. He threw 166 2/3 innings between the minor and major leagues last season for the Miami Marlins. ... Joe Torre and Jim Leyland, representing Major League Baseball, visited with the Angels on Tuesday to deliver an update on various topics, including baseball's use of instant replay.