"The great thing about this game is that you can go from zero to hero," Giambi said. "It could have been a rough night, but you make the night great with one swing of the bat."
"Jason struggled all night," manager Joe Torre said, "but that was the prettiest thing I saw all night."
Mariano Rivera recorded the win with three innings of scoreless relief, needing just 25 pitches in the outing. The three inning stint was his longest in a regular-season game since Sept. 6, 1996.
The Yankees were playing short-handed from the start, as Johnny Damon (foot) and Gary Sheffield (wrist) were on the bench. Their replacements came through, as Andy Phillips knocked in four runs for the Yankees, while Melky Cabrera contributed a career-high four hits.
"Melky has done a great job for us in the leadoff spot. He's responded really well," Torre said. "Philly's getting some at-bats, and we've always wondered if he got at-bats how he'd do. He's a pretty good hitter."
The Yankees actually led the game 5-0 and 6-1, but the Tigers battled back against Aaron Small and the Yankees' bullpen, eventually tying the game in the eighth against Kyle Farnsworth.
"To not fold the tent, to keep fighting, it's an example of what these guys are about," Phillips said. "It was a great team win for us."
The Yankees improved to 30-20, moving 10 games over .500 for the first time this season. Last year, New York didn't reach the 10-over mark until Aug. 8, when the Yanks were 60-50.
New York has won four consecutive games, including two straight against Detroit. With Boston's loss to Toronto, the Yankees moved into a first-place tie with the Red Sox in the American League East.
"There's a lot of grittiness in here and I really like what I feel and what I see," Torre said. "We got a little down after they tied it up, but we jumped right back up and started pulling for each other."
New York didn't appear to miss a beat without their two star outfielders, scoring four times in the second inning against Tigers starter Roman Colon.
Ivan Rodriguez homered in the third to get the Tigers on the board against Small, but the Yankees answered with a run in the fifth, taking a 6-1 lead.
Detroit cut the lead to 6-4 in the fifth, thanks in part to an error by Derek Jeter, who booted a potential double-play ball that helped the Tigers start a rally.
Small's final line saw him allow four runs on seven hits in a season-high five innings. Scott Erickson relieved Small in the sixth, allowing a run to shrink the lead to one run.
Scott Proctor tossed a perfect seventh, but Farnsworth loaded the bases to open the eighth, putting the lead on life support.
Brandon Inge hit a grounder to Jeter, but the Yankees couldn't the double play, as Marcus Thames scored from third to tie the game. Farnsworth stranded the runners at the corners, striking out Curtis Granderson and Placido Polanco to send the game to the ninth tied at 6.
"Farnsworth may have been the key to the whole night," Torre said. "He had the lead run at third base, one out and the top of the order up and he strikes out two guys. He kept it together and gave us a chance to do what we did."
The Yankees had a chance to plate the go-ahead run in the ninth, when Robinson Cano tried to score from third after Fernando Rodney's pitch got away from the catcher. But Rodriguez made a quick play on the ball, flipping it to Rodney in time to tag Cano for the third out.
With the game still tied in the 11th, Giambi crushed Jones' 1-2 pitch into the right-field seats for his 13th homer of the season, his first since May 10.
"I didn't get many mistakes, but luckily Jonesy hung me that breaking ball and I didn't miss it," Giambi said. "It's all about taking good at-bats. If I hit the ball hard, I know that eventually it's going to come around. The product of hitting the ball hard is hitting home runs."
"He's done it so many times, it's incredible," Phillips said. "Guys were fighting and battling all night long, so for him to come through like that, it was huge."
The Yankees added four more runs in the inning, two of them on Phillips' second hit of the night.
Rivera, who threw just four pitches in the ninth, the last of which started a 1-6-3 double play, needed just 12 pitches to get through the 10th. He returned to the mound with the five-run lead in the 11th, and nine pitches later, the Yankees were in first place.
"I was able to do my job, and the guys put some runs on the board," Rivera said. "It's big because of the way we were winning. It's tough to lose a game like that, so I'm glad we won."