Rivera didn't allow a run and Giambi's solo home run sparked a five-run 11th inning to lift the Yankees to an 11-6 victory over Detroit on Tuesday night.
"When his ball is moving like that at 95 or 96, it's almost like you don't have a chance," Detroit outfielder Craig Monroe said of Rivera.
New York manager Joe Torre brought his star closer in for the ninth with the score tied. Rivera was so efficient Torre left him in for two more innings for his longest outing -- other than the 2003 AL championship series against Boston -- since Sept. 6, 1996, when he also pitched three innings against Toronto.
Rivera (3-3) needed just 25 pitches over the three innings to hold off the Tigers.
"He was great," Torre said. "He didn't waste any pitches, obviously.
"If had thrown 15 pitches in that first inning, he wouldn't have pitched the second."
The Yankees, who had a pair of five-run leads before the game went to extra innings, are a season-high 10 games over .500 with their fourth straight win.
"This is a terrific game for us," Torre said. "There's a lot of grittiness in here, and I like what I feel and see."
Despite losing three in a row, the Tigers still have the best record in baseball.
"I told them that I'm proud of them, they battled," Detroit manager Jim Leyland said. "I have absolutely no complaints. God bless them."
Todd Jones (0-2) pitched a perfect 10th before Giambi turned on a hanging breaking ball and sent it into the right-field seats with one out in the 11th for his 13th homer.
"All night, I didn't see much to hit," said Giambi, who his first homer since May 10th. "But Jonesy made the mistake, and I didn't miss it."
The Yankees eventually chased Jones, who had his longest and worst outing of the year. He gave up five runs and four hits with a walk in 1 2/3 innings.
Yankees setup man Kyle Farnsworth entered in the eighth, and the Tigers loaded the bases with two walks and a single against their former teammate.
Brandon Inge then hit a grounder to shortstop Derek Jeter, who flipped it to second baseman Robinson Cano, who couldn't get enough on his throw to first because of Marcus Thames' late slide -- allowing pinch-runner Ramon Santiago to score and tie it at 6.
"To give up only one run with the bases loaded is a big thing," Farnsworth said. "It kept the team in it to win it."
New York led 5-0 in the third and 6-1 on Andy Phillips' sacrifice fly in the fifth, but the Tigers chipped away.
Ivan Rodriguez hit a solo homer in the third, ending a 20-inning scoreless streak for the Tigers and a 25-inning drought against the Yankees, dating to last season.
Rodriguez's two-run triple in the fifth and Magglio Ordonez's RBI single pulled Detroit to 6-4.
Rookie Joel Zumaya, whose fastball reached 101 mph, kept the Tigers in the game by striking out four and giving up only one hit in a career-high 2 1/3 innings.
Rodriguez made a nice play at home in the ninth inning to keep the game tied. Fernando Rodney threw a pitch in the dirt and past Rodriguez. The catcher pounced on the ball, pivoted on his knee and threw to Rodney, who tagged Cano out at home.
Aaron Small allowed four runs -- three earned -- and seven hits with two walks over five innings.
Two of the Yankees' better players were not in the starting lineup.
Johnny Damon, who entered in the ninth as a pinch-runner, didn't start because of continued problems with his foot, which he injured April 18 and aggravated earlier this month. Gary Sheffield was scratched from the lineup just before the game due to soreness in his left wrist, which he hurt a month ago and aggravated during batting practice.
Torre expects Sheffield to miss the last two games of the series against Detroit, and said he didn't think Damon would play Wednesday.
- Small made his second start in place of Shawn Chacon, who is on the 15-day DL with a bruised left leg.
- Maroth, on the 15-day DL, is scheduled to have his left elbow examined Wednesday.
- Tigers manager Jim Leyland, whose family still lives in Pittsburgh, has decided he is not going to buy a house in the area because of high taxes and will continue living in a suburban Detroit hotel during homestands. Leyland occasionally sleeps at Comerica Park.
- Yankees LF Melky Cabrera had a career-high four hits.