Swisher, who entered in the 11th to play first base, hit a three-run homer with two outs in the bottom of the 14th and Chicago rallied for four runs off Joel Zumaya to beat the Detroit Tigers 10-8 on Tuesday night.
"I didn't even really anticipate playing," said Swisher, who was mobbed by his teammates at the plate.
"We scratched and we clawed and we pulled some runs together. I've been talking about that all year long, the will to fight."
But Detroit's bullpen woes continued. Zumaya (0-1) gave up a single to Orlando Cabrera and a double to Carlos Quentin. When Tigers' shortstop Edgar Renteria fumbled Jermaine Dye's grounder for an error, Cabrera scored and the lead was down to one.
After Jim Thome struck out for the second out, Swisher homered into the right-center field seats on a 2-1 pitch. Swisher had entered the game in the 11th after Paul Konerko had been removed for a pinch-runner in the 10th.
"It feels like you're hitting on sound at that point in time," Swisher said of Zumaya's high 90s fastball. "He's one of those guys that obviously throws a very plus-plus fastball. In that situation all I was really trying to do was put the barrel on the ball. He's generating so much power with his fastball if you hit it solidly -- which is rare -- it's going to go a long way."
Ken Griffey Jr. made his home debut with the White Sox after being acquired in a trade from the Reds last week and went 1-for-6 with three strikeouts. He was also unable to cut off a liner to right center by Polanco that went for a triple in Detroit's four-run fifth that built the 6-1 lead.
But he was touched by a standing ovation he got when he first came to the plate.
"I can count probably four other times that it's been like this," he said. "Going back to Seattle. Five-hundred [homers], 600, things like that and now here. And Cincinnati the first time."
After the four-run flurry in the fifth, the Tigers went eight innings without scoring before Polanco -- a career .325 hitter against the White Sox -- delivered his fourth career multihomer game. He also hit a two-run homer in the first inning of the four-hour, 58-minute game.
"When you need two outs to win the game, it's a tough loss," Polanco said. "What can you do? We're all professionals here. Turn the page."
Chicago was without manager Ozzie Guillen, who began serving a two-game suspension for making contact with umpire Tim Timmons and his comments Sunday after the Royals and White Sox had a melee in Kansas City.
The White Sox's victory gave them a one-game lead in the AL Central over the Twins, who lost to Seattle.
The Tigers, who lost their fifth straight, blew a 6-1 lead. They still had a chance to put the game away in the 14th, but Renteria's error was a big one.
"I thought I played the ball perfect," he said. "Everything was right. I don't know what happened at the last moment."
Chicago used its power to get back in the game as Konerko hit a two-run homer in the sixth and Quentin connected on his AL-leading 29th homer in the seventh.
The Tigers turned three double plays early behind Nate Robertson, who failed for the eighth straight start to get his seventh win. In five-plus innings, he allowed four runs and nine hits, including Konerko's 11th homer in the sixth.
Polanco hit a two-run homer after a leadoff walk by Curtis Granderson in the first against Gavin Floyd. Chicago got a run back in the third on an RBI grounder by A.J. Pierzynski but Detroit drove out Floyd in the fifth.
Granderson homered after a leadoff double by Renteria in the fifth. After Polanco's triple, Carlos Guillen followed with an RBI single to finish Floyd, who gave up eight hits and five runs in four-plus innings. Raburn, who had four hits, later delivered an RBI single for a 6-1 lead.
Detroit relievers are just 22-for-42 on save situations. ... Raburn's four hits matched a career high. ... Bench coach Joey Cora was in charge of the White Sox in Guillen's absence.