Staked to 6-1 lead in the second, Garland became the American League's first six-game winner. Garland (6-0) tossed shutouts in his previous two starts, but Shea Hillenbrand ended his 23-inning scoreless streak with a RBI grounder in the first.
Garland allowed six runs and nine hits in 5 2/3 innings. He has won eight straight starts dating to last season, the longest streak by White Sox pitcher since James Baldwin also won eight in a row in 2000.
"They picked me up big-time," Garland said. "I never got into a groove."
Tadahito Iguchi, Juan Uribe and Aaron Rowand also homered to help the White Sox improve their major league-best record to 23-7. Scott Podsednik tied a career high with four stolen bases, previously done with Milwaukee last Sept. 18 at Houston.
"It was kind of weird," Chicago manager Ozzie Guillen said. "We don't have that kind of lineup. The best thing about the home runs was that we had people on base."
"This kid can carry a team for a month. He did it earlier in the season," Guillen said
Konerko hit seven home runs in his first 14 games of the season but went homerless in his next 15 before Saturday. His 172 homers move him past Robin Ventura for the fifth in franchise history.
"It was a matter of time before we busted out. We've played a lot of one-run games, and that can wear on you," Konerko said. "It's nice to get a game where you can coast."
Someone had a little fun with Konerko, too. Just before his second homer, a message on the Rogers Centre board read "Paul likes to take long walks on the beach."
The White Sox extended their major-league record of consecutive games with a lead to 30 when Konerko homered in the first.
Russ Adams homered twice for the Blue Jays, who have lost three straight after winning seven of their previous nine.
"I don't think Garland pitched particularly well, but he pitched well enough to win," Lilly said. "He's one of the best pitchers in the league and today we had an opportunity to beat him."
Uribe and Iguchi each hit two-run homers off Lilly in the second.
Lilly allowed six runs and six hits in just 1 2/3 innings, his shortest outing of the season.
Konerko and Rowand hit consecutive home runs in the fourth off Whiteside, giving Chicago a 10-2 lead.
Adams homered off Garland in the sixth and Luis Vizcaino in the ninth, the first multihomer game of his career.
Toronto manager John Gibbons dropped struggling center fielder Vernon Wells from third to seventh in the lineup. Wells went 0-for-4, dropping his average to .200. ... Toronto Raptors forward Matt Bonner threw out the ceremonial first pitch. ... The White Sox reached a season high in runs.