The series shifts to New York for Game 3 on Friday.
Finley, who helped San Diego reach the World Series last year, drove in two runs with a bases-loaded single in the third, two more with a double in the fifth, then walked with the bases loaded in the seventh for another RBI. Both hits came with two outs.
Matt Williams was 3-for-4 with a double and three runs scored as Arizona earned its first playoff win.
The NL West champion Diamondbacks are the first team to get to the playoffs in their second season.
"The franchise is young but there's a lot of veterans," New York manager Bobby Valentine said. "Stottlemyre tonight seemed to take the bull by the horns, and Finley and Matt, who have been there before, did what they had to do."
The loss was the first in October for the Mets, who won the final four games of the regular season including a one-game wild-card playoff against Cincinnati and the first game against Arizona.
"What we did is win one and lose one, and we'll take that," Valentine said.
Rickey Henderson, the Mets' 40-year-old leadoff hitter, stole second three times to break the NL record for most steals in a division series with five. His three stolen bases in a game tied the major league mark for a division series.
Stottlemyre allowed one run and four hits over 6 2-3 innings. The intense right-hander struck out six and walked five, but battled out of trouble throughout.
"It's not surprising," manager Buck Showalter said. "Maybe some eyebrows were raised when I said Todd was pitching the second game here. But I think tonight you saw why we have so much confidence in him. Todd's a warrior, a baseball player who happens to be a pitcher. Todd's a guy you want to go in tough situations when you need a win."
Stottlemyre, 3-5 in the postseason, threw a complete game for Texas in Game 1 of last year's playoffs against the New York Yankees but lost 2-0. This one was sweeter because of what Stottlemyre went through to get here and because it was a win the Diamondbacks knew they must have.
Stottlemyre is believed to be the only pitcher to come back from a serious rotator cuff injury to pitch again without surgery. He tore 70 percent of his rotator cuff in San Francisco May 17.
At age 34, he decided not to undergo season-ending surgery. Instead, he went through intense rehabilitation, strengthening his upper body, especially the area around the injury, then returned on Aug. 20.
Stottlemyre threw 124 pitches, the most he's thrown all season and 21 more than he'd thrown since coming back from his injury, before being relieved by Gregg Olson with runners at first and second and two outs in the seventh.
After a double-steal put runners at second and third, Olson got first-game hero Edgardo Alfonzo to ground out to end the inning. Reliever Greg Swindell pitched the eighth and ninth to complete the five-hitter.
New York took a 1-0 lead when Henderson led off the top of the third with a single, stole second and advanced to third on a fly out and scored on John Olerud's groundout to shortstop.
New York starter Kenny Rogers allowed four runs and five hits in 5 1-3 innings.
Rogers got two outs in the third before the trouble started.
|The Mets could have used a big game from Kenny Rogers, right, and Mike Piazza.|
With two outs, Rogers walked Greg Colbrunn on a 3-1 pitch to tie the score at one.
Lefties batted only .208 (11-for-53) against the left-handed Rogers since he joined the Mets in July. But Finley lined Rogers' 1-2 pitch to right field for a single.
Gonzalez scored, then Williams slid in just ahead of the tag for the third run. New York manager Bobby Valentine argued that Williams never touched the plate. Replays showed that Williams' lead leg missed the plate but his trailing knee might have touched it before the tag.
Bell led off the fifth with another single. Gonzalez struck out, and that was it for Rogers. Williams hit reliever Pat Mahomes' first pitch up the middle for a single to put runners on first and second. Colbrunn struck out, then Finley doubled to the gap in left-center to score both runners and make it 5-1.
Octavio Dotel walked Finley with the bases loaded in the seventh, then Williams scored on pinch hitter Turner Ward's ground out to make it 7-1.
After three homers in his last two games, including a game-winning grand slam in the ninth on Tuesday, Alfonzo was 0-for-4.
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