Carlos Quentin went 4-for-4 with two homers and four RBIs for the White Sox, who finished with 16 hits. Dye went 3-for-5, and Konerko had four hits and three RBIs.
Dye and Konerko became the first teammates to hit century milestone home runs of at least 300 in the same game, according to Elias Sports Bureau.
"We talked about starting a pool or something of who would get there first in the dugout before the game," Konerko said. "We probably would have if it had went one more day."
Dye hit a 2-1 pitch from Zach Miner (1-1) over the wall in left-center leading off the second. Konerko went deep on a full-count offering to make it 2-0. It was the second homer of the year for both.
"I think we're just good hitters with power," Dye said. "I think we both hit a lot of line drives that are able to get out of the ballpark. You look at Jim [teammate Jim Thome] and he's 250 ahead of us. So I don't know if you can call us home-run hitters."
Chicago added four more in the third. Quentin singled in a run, Konerko doubled in a pair and Alexei Ramirez's RBI single made it 6-1.
The White Sox won their third straight game but lost center fielder Dewayne Wise to a separated shoulder in the fifth. With runners on first and second and Chicago leading 8-4, Wise robbed Santiago with a fine grab in deep right-center field. Anderson doubled in two runs for the Tigers later in the inning.
"I think he saved the game," Chicago manager Ozzie Guillen said of Wise's catch. "When he made that play, that was the game right there."
Wise was replaced by Brian Anderson. Guillen said he would be out four to six weeks.
Miner allowed eight runs and nine hits, including three homers, in 3 1/3 innings.
"Zach had a bad day, a terrible day," Tigers manager Jim Leyland said.
Gavin Floyd (1-1) lasted five innings to get the win. He gave up six runs and five hits, walked seven and struck out two.
"Just really tried to keep our team in the ballgame," Floyd said. "Just one of those games I didn't feel great."
Santiago's two-out drive in the third cut Chicago's lead to 6-4 but Quentin responded with a two-run shot in the fourth. He hit his fourth homer of the season in the sixth and Konerko doubled in Dye to make it 10-6.
Anderson singled in a run in the second for his first hit and RBI with the Tigers.
Former Detroit pitcher Mark "the Bird" Fidrych was found dead Monday in an apparent accident at his Northborough, Mass., farm. He was 54. The colorful right-hander was the AL Rookie of the Year in 1976 when he went 19-9 with a 2.34 ERA. He spent all five of his major league seasons with the Tigers, compiling a 29-19 record and a 3.10 ERA. ... Detroit acquired Anderson in a trade with the Atlanta Braves on March 30. ... Chicago 2B Chris Getz, who is from the Detroit suburb of Southfield, missed the game with a stiff elbow. ... Tigers C Gerald Laird missed the game because he was ill. ... Detroit relievers' streak of 26 consecutive batters retired was snapped when Konerko led off the fifth with a single.