After going hitless in five previous at-bats and striking out with the winning run at third base in the 10th inning, Thome launched a home run with one out in the 15th inning off Justin Speier to give the Sox a heartening 7-6 victory over the Los Angeles Angels.
The Sox celebrated wildly as they expanded their lead in the American League Central to 21/2 games over Minnesota, which lost to Detroit shortly before the Sox took the field.
"It makes it a big win for us right there," said reliever Matt Thornton, who pitched 22/3 scoreless innings.
Thome's homer was the 537th of his career, passing Mickey Mantle for sole possession of 14th place on the all-time list.
"Those names are icon names," said Thome, who also has passed Jimmie Foxx, Ted Williams and Willie McCovey this season. "It's kind of surreal to be in a group of that many great players. You appreciate it, but you have to move on. We're in the middle of a pennant race."
And the Sox nearly didn't get a chance to celebrate after stranding the winning run in scoring position in the ninth, 10th and 11th innings.
"That's Jim's fault we played that many innings," manager Ozzie Guillen joked. "He got the revenge."
Guillen was proud the Sox rallied from three deficits and that relievers Mike MacDougal, Horacio Ramirez, Ehren Wassermann and Thornton combined for five scoreless innings after Brandon Wood hit the go-ahead home run off closer Bobby Jenks in the ninth.
"We have to step it up," Guillen said. "Hopefully we're back to having the bullpen we had earlier."
Konerko hit home runs in consecutive games for the first time since Sept. 27-28, 2007. His is hitting .412 (14-for-34) in his last nine games.
Wood's homer was the first Jenks has allowed since May 9, when Wladimir Balentien hit one off him in Seattle.
But the Sox rebounded to tie the game 6-6 as Alexei Ramirez singled and Swisher singled him to third.
Pinch-hitter Dewayne Wise's sacrifice fly tied the game, but pinch-runner Jerry Owens was nailed trying to move up to second.
Thome then struck out, Pierzynski was caught off third on a Konerko grounder and Ken Griffey Jr. flied out deep to center.
In the 11th, Pierzynski struck out with the tying run on, but the frustration turned to elation when Thome hit the Sox's fifth game-ending homer of the season.
"It has been great to watch him over the past few years," Thornton said. "That was one of his best."