To cap it off, Mariano Rivera nailed down career save No. 400, making him just the fourth player in history to reach that number.
"We did everything we could for perfect baseball," Jason Giambi said. "I think it was, by far, our three best games."
The Yankees have now won seven of their past eight games and also crawled to only three games back in the American League Wild Card race behind the White Sox.
"Taking nothing away from Detroit, but [the White Sox are] pretty [darn] good," manager Joe Torre said. "I don't think you're going to be tested any more so than we have this weekend."
With Johnny Damon on the bench with calf cramps and Gary Sheffield and Hideki Matsui still out, the Yankees' starting outfield entered the game with 41 combined RBIs this season. Bubba Crosby was in center field, Aaron Guiel was in right and Melky Cabrera manned left.
The Yankees also sent No. 4 starter Jaret Wright to the mound. Wright wasn't spectacular, as he gave up three earned runs in 5 1/3 innings.
The White Sox could have easily avoided a sweep, which was their first since Sept. 11, 2005. They were 2-for-15 with runners in scoring position, but a large part of that was because of the Yankees' defense.
The pressure started early as Wright walked the game's leadoff batter, speedy Scott Podsednik, then gave up a single and RBI double to Jim Thome to spot the White Sox a quick 1-0 lead.
The next batter, Paul Konerko, bounced a ball to Alex Rodriguez, who alertly threw home to save a second run from scoring. On the next play, Rodriguez ranged far to his right but still pulled off a double play to end the inning with limited damage.
"That play in the first inning that Alex started really set the tone for us," Torre said. "It got us feeling good about ourselves although we're one run behind."
Derek Jeter quickly fixed that, hitting a long homer to left field off White Sox starter Freddy Garcia in the bottom of the first. It was Jeter's first home run in 189 at-bats since May 16, the second-longest stretch without a homer in his career. Giambi then walked and Rodriguez hit a homer of his own to put the Yankees up, 3-1.
Wright had trouble in the third, which again began with walking Podsednik to start the inning. Tadahito Iguchi singled and Thome bounced into a fielder's choice to put runners at first a third. Konerko followed with hard liner just past the diving Miguel Cairo.
Cairo's near catch forced Thome to hesitate on the basepaths and gave Guiel time to charge the ball and throw out Thome at second. What could have been a big inning for Chicago was once again avoided.
"A good defensive player will think of situations before they come up," Guiel said. "So that's one that you think about. As soon as I see the runner break back, I know I've got a good chance."
The Yankees scored again in the third and pushed across two more runs on RBIs from Cairo and Crosby in the fourth to make the score 6-2 in the fourth. But the pesky White Sox continued to stick around.
After a sacrifice fly made the score 6-3, Joe Crede tried to score on a single to left field. Cabrera fielded the ball as Crede touched third base and gunned him out at home with a perfect throw to end the inning.
The White Sox had two runners on base with no outs in the seventh before Mike Myers used one pitch to retire Thome. Kyle Farnsworth then got two straight flyouts to get out of the inning.
Farnsworth hit a wall in the eighth, leaving with runners on first and second and again no outs. That's when the bullpen doors opened and the fans roared as Rivera jogged to the mound to go for No. 400. Rivera used a double play and just seven pitches to get the three outs.
In the ninth, the White Sox got their first two hitters in on base for the third straight inning. But Rivera got a double play and struck out Jermaine Dye swinging to get his milestone save.
"Everybody's paying attention and everybody's into it," Torre said. "Usually, when it gets hot like this, you have guys dragging a little bit, but these guys were battling through it. I know they're proud of themselves and they should be. They beat a very good team this weekend."