CHICAGO -- After a terrible start, Dan Johnson and the rest of his Oakland teammates can't complain about the way they finished the first half.
Swisher also homered, and Johnson hit a solo homer and a two-run double for the A's, who finished the season series against the White Sox with a 7-2 record and have won 13 of their last 16 games overall. They also moved one game over .500 for the first time since May 1, when they were 13-12.
The A's were 15 games under .500 on May 29.
"We had such a slow start in May. We get above .500 going into the All-Star break," Johnson said. "Taking this momentum going into the second half, we have our division coming up. We need some momentum going into those series."
Carl Everett and Paul Konerko homered for the White Sox, who took a 57-29 record into the All-Star break but were swept in a three-game series for the first time this season. Konerko set a new career high with five hits.
"It was a really disappointing weekend, but there is nothing you can do about it," White Sox manager Ozzie Guillen said. "One of the best things we've done all year, every time we got a losing streak, we bounced back and played pretty good baseball. I expect the same thing when we come back in a couple of days."
Luis Vizcaino (3-3) walked Eric Chavez to start the 11th and gave up an infield single to Johnson. Bobby Kielty moved both runners up with a sacrifice bunt and Swisher followed with a double to right-center to score Chavez. Johnson was thrown out at that plate on Willie Harris' relay throw.
"We kind of figured something out," said Chavez, who also got off to a slow start. "I think the pitchers have confidence and the hitters are scoring runs. The first two months, we weren't really doing that. Right now we're just playing well and have to keep it going."
Huston Street (3-1) got his fourth blown save of the season but shut out the White Sox in the 10th and 11th. He threw a career-high 3 1/3 innings.
"He was out there throwing as hard as he ever was. I don't know how many times he's been out there for three innings," Oakland manager Ken Macha said.
"It just shows you what he's made of. He didn't get down. They hit a home run off him, he stayed within himself, came back and got the job done. we got the win and he did what he was supposed to do."
White Sox slugger Frank Thomas was impressed with the A's pitching and timely hitting.
"As for what they did on the field, they got guys over, they stayed in a zone, they put the ball in play and it seems like everyone was bubbling at the same time," Thomas said. "So it's hard to beat a team when everybody is hot at the same time and the pitching staff is pitching well. Today we really wanted that win, but they found a way to suck it out of us."
With Oakland leading 8-6, Street gave up a leadoff home run to Konerko in the ninth. Everett followed with a single and moved to second on Aaron Rowand's sacrifice bunt. A.J. Pierzynski struck out looking, then was ejected after flipping his bat in front of home plate umpire Marty Foster.
After Guillen had a lengthy discussion with Foster and crew chief Dana DeMuth, pinch-hitter Timo Perez followed with a RBI double to tie it.
Trailing 5-4 in the seventh, Oakland came back to take the lead with three runs against reliever Neal Cotts. The White Sox cut the lead to 7-6 in the seventh with a RBI single by Pierzynski off Justin Duchscherer.
Oakland led 4-2 in the fourth behind Dan Haren, but consecutive errors by Chavez and Johnson helped Chicago score a run. The White Sox took the lead off Haren in the fifth when Konerko singled and Everett followed with a homer to right, giving the White Sox a 5-4 lead.
Haren pitched 5 1/3 innings, allowing five runs -- four earned -- and 10 hits. He has not lost since May 26 against Tampa Bay.
White Sox starter Freddy Garcia allowed a run in each of the first four innings. He pitched six innings, allowing four runs on nine hits.
Johnson led off the third with his fourth homer of the season, giving the Athletics a 3-1 lead. Kotsay homered with two outs in the fourth, his second homer in two days and eighth of the season, to give Oakland a 4-2 lead.
- White Sox 3B Joe Crede missed his second straight game with a sore back.
- Since going 6-3 against the A's in 2000, the White Sox are 11-33.
- The A's matched their season high with three errors.
- After the game, the White Sox optioned LHP Kevin Walker to Triple-A Charlotte.