It was Detroit's second straight win over the AL Central leaders, who lost for the fifth straight time on the road.
Verlander (3-9) didn't walk a batter and struck out three. He threw 101 pitches in his best outing of what has been a disappointing season for himself and the Tigers.
Chicago had been the only team he had trouble against in his first two seasons. He was 1-6 with a 6.14 ERA against the White Sox coming into the game.
"Those guys have had my number for two years, so it's nice to be able to go out and give the team a lift when they needed it," Verlander said.
He retired the first nine Chicago batters as they continually swung at the first pitch. Verlander relied almost exclusively on fastballs the first three innings.
"He had electric stuff tonight," said Chicago outfielder Brian Anderson, who had two hits. "We helped him out by swinging at a lot of first pitches and keeping his pitch count down. He just pounded the zone with strikes. When a pitcher does that to you, it's going to be a short night."
Verlander mixed in his changeup for his first complete game since his no-hitter over Milwaukee last June 12.
White Sox starter Javier Vazquez (6-5) gave up five runs and 10 hits in six innings, walking three and striking out nine.
"When he made a mistake, we capitalized," Tigers manager Jim Leyland said.
Thames' three-run homer in the second gave Detroit a 3-0 lead.
After being down 0-2 in the count, Miguel Cabrera worked Vazquez for a 14-pitch walk to lead off the second. One out later, Edgar Renteria's infield single sent him to second. Thames then drilled Vazquez's first pitch over the left-field fence for his seventh home run.
"I just tried to look for something out over the plate," said Thames, who before the game told Verlander: `'I'll do something for you.'"
He proved to be a man of his word.
"I put us in a big whole with that three-run homer to Thames," Vazquez said. "When you do that it's a killer."
Chicago made it 3-1 in the fourth on A.J. Pierzynski's RBI single. Orlando Cabrera led off the inning with the White Sox's first hit of the game, a ground-rule double down the third base line. Pierzynski followed with a looping liner down the right-field line to score Cabrera, but was thrown out at second trying for a double.
Detroit RHP Jeremy Bonderman, on the DL with thoracic outlet compression syndrome, will be examined on Tuesday by Dr. Greg Pearl in Dallas. ... White Sox manager Ozzie Guillen briefly chatted before the game behind home plate with Chris Chelios of the Stanley Cup champion Detroit Red Wings. ... Tigers DH Gary Sheffield, who is on the DL with a left oblique strain, hit before the game for the second consecutive night. He said he felt a little spasm Tuesday night, but that it was nothing big.