After losing the first two games of a four-game series, the World Series champions were pleased a split kept them in the division race.
"This was huge," Garland acknowledged. "After losing the first two, we had to salvage these two. Now, we've still got a chance."
Chicago trails Detroit by 5½ games in the division and has a slim lead over Minnesota in the wild-card race.
"I don't say that we're in big trouble if we lose today, but now we can go back to Chicago and take care of our business," manager Ozzie Guillen said.
The White Sox head home for a three-game series against the Twins, who likely will not face designated hitter Jim Thome, who strained his left hamstring Wednesday night.
Detroit had a 10-game lead after play on Aug. 7, but the cushion has been cut almost in half after losing 11 of 16 games.
"We'll find out if we're good enough," Tigers manager Jim Leyland said.
Garland (15-4) struck out two and walked one in his fifth career shutout, his third against Detroit. His previous shutout was Sept. 4 last year against -- who else? -- the Tigers.
"That's as good a pitching game as we've had all year," Guillen said. "He did everything that a pitcher is supposed to do out there."
Nate Robertson didn't.
Robertson (11-10) gave up a career-high 10 runs and nine hits in 6 2/3 innings. He has lost four of five starts, though his previous four were solid.
"He made a lot of bad pitches and every one of them went out of the ballpark," Leyland said.
Chicago scored one run in both the first and third innings before turning the game into a rout with three in the fourth, two in the fifth and three more in the seventh.
"They looked like they were having fun, and we looked tired," Leyland said. "When you have a real ugly game, it's usually a combination of bad pitching, hitting, managing and defense -- we had all of that."
Leyland was not upset with first baseman Sean Casey after a bizarre play in the fifth, but was disappointed with some fans' reaction and a reporter's question about it.
Casey hit a liner to third baseman Joe Crede, then stopped running and pivoted toward home when it appeared the ball was caught before sprinting to avoid an embarrassing putout. Left fielder Pablo Ozuna charged and made a bouncing throw that just beat Casey.
"The people behind the dugout were booing and teasing him for not running," Leyland said. "That to me is not a fan."
Garland said the 5-7-3 play was a sign of things going Chicago's way.
"That's probably never happened before," he said.
Dye's homers -- in the first and fifth innings -- and Juan Uribe's all were two-out shots.
"When you come into this town and split a four-game series, the way that team is going, it's satisfying," said Dye said, who finished 3-for-3 with a walk, a double, three RBI and four runs.
Uribe's three-run homer in the fourth put the White Sox ahead 5-0 and Ozuna had three of Chicago's 14 hits.
"That's the best lineup in baseball, even without Thome," Robertson said.
- Over the last two seasons, Garland leads the AL with 33 wins.
- Garland is 4-1 with a 2.52 ERA in his last five starts.
- A sellout crowd of 41,565 put the Tigers over the 2 million mark for the third time since Comerica Park opened in 2000 and the ninth time in team history.
- Detroit CF Curtis Granderson ended an 0-for-21 streak with a single in the first inning.
- Over the last 49 games, Dye is hitting .366 with 17 homers -- four of which came in the series.
- The game started after a rain delay of 55 minutes.