The Tigers used three early homers and three late defensive gems to beat the Yankees 5-4, and can win their first series since mid-July with a victory in the series finale Monday night.
"We've had some bad moments this year, but the one thing about this team is that they always give it everything they have," Tigers manager Jim Leyland said. "That's the thing that makes a manager proud."
The Tigers moved within 5½ games of the Seattle Mariners in the wild-card race. Detroit began the day 2½ games behind Cleveland in the AL Central.
"We knew how much we needed this one," said Tigers reliever Joel Zumaya, who pitched 1 2/3 scoreless innings. "A big game against the Yankees means a lot of emotion."
New York fell 2½ games behind Seattle, and seven behind Boston in the AL East.
"We're all right," manager Joe Torre said.
Hideki Matsui started the inning with a grounder between first and second, but Guillen, who moved from shortstop to first before the eighth inning, ranged far to his right to get the ball, then threw across his body to Jones covering first.
"That was an incredible play," Jones said. "I didn't think he could get to the ball, but when he did, I figured I better get myself over to the bag."
"They caught everything we hit," Torre said. "With our offense, normally we can overcome that."
Guillen, Detroit's All-Star shortstop, has been playing first base in the late innings of games because of a bad back.
"I'm comfortable there," said Guillen, who started playing first base in last year's World Baseball Classic. "I'm just trying to enjoy it and do the best I can."
Bobby Seay (1-0) was awarded the win after pitching two scoreless innings of relief. The Tigers needed five pitchers after rookie starter Jair Jurrjens left in the second inning because of a sore shoulder.
"It's been a long time coming," said Seay, who hadn't won since 2001. "This feels good."
Phil Hughes (2-2) lost for the first time since his major league debut on April 26. He allowed five runs and four hits, including three homers, in six innings. He walked one and struck out six.
"We lost, so it was a bad start," he said. "That's the only way you can look at it."
The Tigers had only four hits in the game, none after the third inning.
Curtis Granderson, who leads the majors with 21 triples, led off the Detroit first with an inside-the-park homer. Granderson hit a slicing liner down the left-field line that got by Matsui and rolled to the wall, and he easily beat Alex Rodriguez's relay to the plate.
"Once it got by Matsui, I was thinking about third, but then I saw Gene Lamont waving," he said. "He kept waving and I kept running."
Placido Polanco singled, and after Hughes retired the next two hitters, Guillen homered deep into the right-field stands.
Giambi made it 3-1 in the second with a homer that landed in almost the same spot as Guillen's. Jurrjens left the game without throwing another pitch, and was replaced by Chad Durbin.
Marcus Thames gave the Tigers a 5-1 lead in the third with a two-run homer, but Cano made it a one-run game with a three-run shot off Durbin in the fourth.
The Yankees put two runners on with one out in the fifth, but Seay replaced Durbin and retired Bobby Abreu and Alex Rodriguez to end the inning.
Inge started Detroit's defensive show when he robbed Melky Cabrera of a leadoff single in the eighth. Cabrera's hard bouncer up the middle deflected off Zumaya's glove and rolled toward the third-base line, but Inge made a barehanded pickup and threw Cabrera out at first.
Zumaya, in his third outing since returning from the disabled list, then retired Abreu and struck out Alex Rodriguez to end the inning. He was activated Tuesday after missing more than three months because of a sprained middle finger.
"I haven't had a strikeout in a while, so it felt really good to get A-Rod," he said.
- Granderson was the fourth Tiger to hit an inside-the-park homer in Comerica Park's eight seasons.
- The game was delayed for approximately five minutes while Durbin warmed up after Jurrjens' injury.
- Cano's homer, which landed in the bushes beyond the center-field fence, was estimated at 431 feet.
- Polanco extended his major-league record streak of errorless games at second base to 150.
- Jurrjens was placed on the 15-day disabled list after the game with inflammation in his right shoulder.