It was a rough night all-around for the Angels, who put left fielder Vernon Wells on the 15-day disabled list after the game. Wells strained his groin while running out a grounder. The three-time All-Star is on the DL for the fifth time in 13 major league seasons, and first time since 2008.
"It's tough. He was just starting to feel his swing a little bit," Angels right fielder Torii Hunter said. "That veteran presence — we need him in the lineup. Him and Kendrys (Morales) being out, it's killing us. But we'll keep doing what we need to do. We've got some young guys stepping up."
Jackson (3-4) scattered five hits, struck out five and walked one after going winless in his previous five starts since beating Tampa Bay 5-1 on April 7.
"He threw a whole lot of off-speed pitches," Angels first baseman Mark Trumbo said. "I'd say his off-speed pitches outnumbered his fastball considerably, and he threw enough of them for strikes. He's also got a good slider and it comes out of his hand like a fastball, so it's really hard to lay off of for right-handed and left-handed hitters.
"Our scouting reports said that he had pretty good command on the outside corner of the plate, so I was kind of looking out there the whole game. But I saw only two fastballs on 12 pitches, so hats off to him for executing his slider."
Jackson was more than grateful for the offensive support after four consecutive outings in which his teammates failed to score while he was in the game.
"It was definitely a great feeling," he said. "When you look up and you have early run support, you don't have to be as perfect and you can attack the hitters. When the offense is swinging like that, you just want to get them back in as quick as possible so they can continue to swing."
Santana (1-4) gave up five runs and eight hits in six-plus innings, including Beckham's two-run homer in the second and Ramirez's leadoff drive in the seventh. Both home runs came on the first pitch.
"The last couple of days we started to swing the bat better, and we carried it into today's game," White Sox manager Ozzie Guillen said. "We did a great job making Santana throw a lot of pitches, got some good pitches to hit and took advantage of that. Santana's been tough against us a lot of times, but tonight we made him throw the ball around the plate."
Santana, who won 17 games last season, saw his ERA climb from 4.43 to 4.81. In his previous start last Wednesday at Boston, the right-hander pitched no-hit ball through four innings before a 2-hour, 35-minute rain delay ended his night.
"Ervin had a couple innings he couldn't finish off," manager Mike Scioscia said. "I think he has pitched much better than some of his internal numbers are indicating. He hasn't gotten on that roll we saw from him last year. But it's in him. No doubt, it's in him."
Quentin, who had a pair of two-out, run-scoring doubles in the third and fifth, made it 8-0 in the seventh against reliever Trevor Bell with his eighth home run after the right-hander relieved Santana and gave up a double to Adam Dunn and a walk to Paul Konerko.
The Angels, shut out in each of Santana's last three losses, got only one runner as far as third base against Jackson. That was in the fourth, when Wells stranded Bobby Abreu with a grounder to third. Wells pulled up limping less than halfway down the line and had to come out of the game.
Jackson got into another jam in the sixth, but Hunter ended the threat by grounding into a double play for the 12th time this season, the most in the majors.
Chris Sale and Will Ohman each worked an inning to finish the six-hitter.
NOTES: White Sox RHP Jake Peavy, who had another bullpen session Monday, is scheduled to come off the disabled list Wednesday to make his season debut in the series finale. The 2007 NL Cy Young Award winner hasn't pitched for Chicago since July 6, 2010, when he faced the Angels and came out after 1 2-3 innings because of a shoulder injury that required surgery. ... Wells is batting .183 with four home runs and 13 RBIs in 35 games. The three-time Gold Glove winner was acquired from Toronto on Jan. 21 with four years and $86 million remaining on a $126 million, seven-year contract he signed with the Blue Jays. ... Santana notched his 900th career strikeout when he got Alex Rios swinging to end the fifth inning. ... Angels 2B Howie Kendrick, who is 1 for 13 against Jackson, was not in the starting lineup for only the second time in the team's first 36 games. Kendrick entered in the fifth, as Alexi Amarista shifted to LF following Wells' injury.