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Callaspo also had a pair of sacrifice flies to give him five RBIs on the day. Mark Trumbo added his 10th homer for the Angels, who finished with a season-high 17 hits less than 24 hours after Chris Sale shut them down for the second time in six days with a 3-0 win.
"No game is ugly. It's just a game, no matter how you win it or how you lose it," Angels slugger Albert Pujols said. "I mean, you look at their ballclub and there's no easy out on their side, either. But when we get it going, we're a pretty good ballclub and we can score runs at any time in the game."
Robert Coello (1-0) recorded his first major league victory, retiring all five batters he faced and striking out three after another ineffective performance by Blanton.
"Those were five huge outs to get in the middle of the game, and we need that kind of contribution from our bullpen," Angels manager Mike Scioscia said. "He's got a really good out pitch, he's got life on his fastball, and he throws strikes. That's a good combination."
Hector Gimenez had four hits and three RBIs for the White Sox, who allowed only 10 runs during their winning streak. Paul Konerko and Alexei Ramirez had three hits apiece, and Adam Dunn drove in two runs before leaving in the fifth because of back spasms.
"I felt it in the on-deck circle before my last at-bat," Dunn said. "I was going through my same stretching routine, and when I came up it just grabbed. I didn't take any warm-up swings. I don't think I've ever had a back spasm before, and I didn't really know what it was. My big concern after that was defensively. I wasn't sure if I was going to be able to get down to get a ground ball - or even worse, get up to do something with it. It never did loosen up."
Chicago was only down by one before Los Angeles broke it open in the seventh against Donnie Veal, who was just recalled from Triple-A Charlotte. Callaspo greeted the left-hander with a drive to left for his third homer, and No. 9 hitter J.B. Shuck made it 10-4 with a two-run double.
Nate Jones (0-4), who came in after Hector Santiago was knocked out in the fourth, allowed four runs and three hits in 3 1-3 innings. Veal was charged with the same totals while recording just one out.
But Los Angeles gave Frieri a couple of insurance runs in the bottom half on Howie Kendrick's RBI single and Callaspo's second sacrifice fly, and the right-hander struck out the side in the ninth to get his eighth save in nine attempts.
Blanton gave up four runs and 11 hits in 4 1-3 innings. He is 0-7 with a 6.62 ERA in his first nine starts with the Angels, who signed him to a two-year, $15 million contract in December.
"I went as hard as I could for as long as I could," Blanton said. "I was just trying to keep putting up as many zeros as possible and keep making pitches."
Coello came on with the bases loaded and one out in the fifth and struck out Ramirez and Alex Rios. The Angels grabbed a 5-4 lead in the bottom half on Trumbo's RBI double and Callaspo's sacrifice fly. Pujols started the rally with an opposite-field double down the first base line against the shift.
"I just closed my eyes when I hit that ball and it went past the bag," Pujols joked. "I know I can hit the ball the other way anytime I want to. Obviously, when they do that, they try to get in your brain and think you're going to change your swing. But you can't do that. You have to stick with it. You have to see the ball and just put your best swing on it."
Santiago was charged with three runs and four hits in 3 1-3 innings. He issued a season-high four walks and struck out two.
Blanton, who has allowed a major league-worst 86 hits, gave up a pair of singles in each of the first three innings. In the first, he escaped unscathed by striking out Dunn and Konerko. In the second, he fielded a high chopper by Dewayne Wise and threw him out. In the third, Blanton got out of the jam by striking out Conor Gillaspie with his 50th pitch.
"He made a couple of pitches to limit the damage and keep his team in it. Then their offense came alive and it turned out to be kind of a slugfest," Konerko said. "It was a long tough game and a tough one to lose. But the guys had some good at-bats."
- Callaspo came within one RBI of tying his career best, set on April 18, 2010, at Minnesota while playing for Kansas City.
- Angels RF Josh Hamilton was in Scioscia's original lineup, but got scratched with no other explanation than a day off to recharge, according to a club spokesman. Hamilton hit for Brendan Harris in the seventh and singled to bring his average up to .214.
- Hamilton was replaced defensively by Trumbo -- who had been slotted as the designated hitter. Instead, Pujols was shifted from 1B to DH and Harris was inserted at 1B.