The result was their first doubleheader sweep since 2009, winning Game 1, 8-4, and Game 2, 7-5, to move to 3 1/2 games back of the first-place A's in the American League West and improve to 12 games over .500.
They've completed 82 games, and can't find much to complain about the first half.
"It's been going great," second baseman Howie Kendrick said. "We've been winning games, and we're right in contention. And that's where you want to be, especially as you're starting to cross the halfway point. We don't feel like we have to catch up this year."
In the opener, Mike Trout, Albert Pujols and Josh Hamilton homered in the same game for the second time ever and Garrett Richards bounced back brilliantly from a first-inning three-run homer by Jose Abreu, retiring 23 of the next 25 hitters to notch eight innings of three-run ball.
Jered Weaver scuffled in the finale, surrendering a couple of big homers -- a two-run shot by Conor Gillaspie in the second and a monstrous three-run shot from Dayan Viciedo in the sixth -- and exiting after just 5 2/3 innings. But the offense strung together 12 hits, and Mike Morin, Kevin Jepsen, Jason Grilli and Joe Smith set down 10 of the 11 batters they faced.
"I just left a couple pitches up, and those guys put it where they should," said Weaver, who has already allowed 16 homers, third-most in the American League and one shy of his total from last year. "But the story of the night was the offense, kept scoring and picking me up, and the bullpen came in and did a great job, so it was good to see."
Ten different hitters drove in at least one run over the course of the doubleheader for the Angels, who are hitting .388 with runners in scoring position over their last seven games.
"That's how you gotta win," Kendrick said.
New lefty Rich Hill -- acquired from the Red Sox for cash considerations on Tuesday -- loaded the bases with none out in the ninth before Smith got a couple of key groundouts in Game 1, then walked his only hitter in the sixth before four relievers pitched 3 1/3 hitless innings in Game 2.
"I did not throw the ball well at all," Hill said. "I'm looking forward to getting back and taking ownership of better outings."
The Angels could survive it on Tuesday, because they hit, because other arms stepped up and because they defended. Defensive specialist John McDonald closed out Game 1 with a couple of slick plays at third base, starting a 5-3 double play and making a charging play on the run. And Erick Aybar turned Game 2 with his glove in the eighth, leaping full extension to snag Viciedo's liner and then ranging up the middle to start an inning-ending, 6-4-3 double play.
"You couldn't go much higher for that line drive," Angels manager Mike Scioscia said. "And the line drive back at Jason, it hit off his glove and Erick just stayed with it, didn't panic, nice feed to Howie who made a nice turn. That's a big play to clean up that eighth inning."
Scioscia's Angels have won 10 of their last 13 overall and all five against the White Sox (39-46) this season.
Trout finished the long day 3-for-8, hitting a key three-run homer in Game 1 and putting on a baserunning clinic in Game 2. Calhoun went 2-for-7 with three walks and a two-run homer in the finale. Hamilton went 3-for-6 with three walks. Chris Iannetta went 2-for-2 with two RBIs and two walks in Game 1. And Kendrick went 2-for-3 in Game 2, scoring a couple of runs and driving in a couple more.
It was a team effort. Truly.
"All in all," Scioscia said, "two really good games."