"To say this is another win is not true," Franco said. "Everybody knows this is not another three-game series before the All-Streak break."
The World Series champions had won 124 consecutive games when they led entering the ninth, but Mariano Rivera (2-2) couldn't hold it.
"Ninety-nine percent of the time, we have a lead in the ninth, we win. It just didn't happen," said Derek Jeter, who went 0-for-4 in his first game as a cleanup hitter.
Mike Piazza hit a big three-run homer for the second straight day, a 482-foot rocket off Ramiro Mendoza in the seventh that landed on a tent behind the left-field bullpen and put the Mets ahead 7-6.
But Jorge Posada's second homer, a two-run shot off Dennis Cook, gave the Yankees an 8-7 lead.
"It was just like a heavyweight fight," Mets manager Bobby Valentine said. "Last guy standing wins."
Rickey Henderson, who went 3-for-3, drew his second walk of the day with one out in the Mets ninth.
Edgardo Alfonzo followed with a high fly that appeared to glance off the glove of a leaping Bernie Williams in left-center. Playing in an unfamiliar ballpark, Williams seemed unsure of where the wall was, and the ball fell for a double that sent Henderson to third.
"I couldn't feel the wall and tried to get there as soon as I could," Williams said. "I'm pretty frustrated right now. It was an emotional game."
John Olerud bounced to first as the runners held and Piazza, whose three-run, tiebreaking homer gave the Mets a 5-2 win Friday night, was intentionally walked.
Franco, batting for Melvin Mora, fell behind 0-2 i the count and then took a pitch just low for a ball.
"My heart stopped a bit," Franco said. "It was close. I've taken that pitch and been rung up before, no doubt about it."
Yankees manager Joe Torre shouted at plate umpire Jeff Kellogg from the dugout.
"It wasn't low," Torre said later. "I can't tell you inside or outside, but it wasn't low."
Franco hit the next pitch for a sharp single to right, and Alfonzo easily beat Paul O'Neill's throw for the winning run. Franco is 11-for-37 (.297) as a pinch-hitter this season with nine RBIs.
"This is the biggest of my career so far -- definitely," a grinning Franco said.
Rivera blew a save for the third time in 25 chances. The Yankees hadn't lost a game they led after eight innings since May 14, 1998, a 7-5, 13-inning loss to Texas.
"We need this game. Kind of sad the way we lost it," Rivera said. "I thought I had him."
Pat Mahomes (3-0), the sixth Mets' pitcher, escaped a two-on jam in the ninth.
"We shot everything we've got," Valentine said.
Since losing their opening two games against the Yankees last month and falling to 27-28, the Mets have gone 23-10, including three straight over the Yankees.
The Mets clinched a three-game series against the Yankees for the first time in four tries.
In addition to Posada, O'Neill also homered twice for the Yankees, who hit six homers for the first time since 1990. Ricky Ledee and Chuck Knoblauch homered once each.
But it wasn't enough, and Mets came back from 2-0, 6-4 and 8-7 deficits.
"You still need to pitch," Torre said. "We didn't get enough outs."
O'Neill, who also doubled, went 3-for-5 with three RBIs. The former Cincinnati Red is hitting .364 (40-for-110) at Shea Stadium with seven homers and 18 RBIs. It was his second multihomer game this season, the 14th of his career.
Shea Stadium was filled with another sellout crowd, this time 53,792, and there was at least one brawl in the stands on a hot and humid afternoon.
Mets starter Rick Reed, 0-2 in five starts against the Yankees, gave up four runs and five hits in five innings. Andy Pettitte, coming off consecutive losses, allowed four runs and five hits in six innings.
"We're doing some little things that end up beating us," Pettitte said.
O'Neill's two-run homer put the Yankees ahead in the first but Piazza, who drove in four runs, hit an RBI double in the bottom half after fouling off six straight pitches. The first of Rey Ordonez's two sacrifice flies tied it in the second, scoring Roger Cedeno, who walked and raised his major league-leading steals total to 45 by swiping second and third.
The Mets then went ahead 4-2 in the fifth on Robin Ventura's RBI double -- a ball Ledee could have caught in left -- and another Ordonez sacrifice fly. Venturslid under the tag by Posada following O'Neill's strong throw.
Ledee and Posada hit consecutive homers in the fifth to tie it at 4. Ledee's was his first in 47 games since connecting against Baltimore's Scott Erickson on June 15, 1998.
O'Neill homered on Greg McMichael's second pitch for a 6-5 lead in the sixth, and Knoblauch got his off Rigo Beltran in the seventh.
- The Yankees hadn't hit six homers since May 23, 1990, at Minnesota.
- The Yankees hit consecutive homers for the third time this season. O'Neill and Bernie Williams did it against Cleveland on June 1, and Chili Davis and Scott Brosius did it Wednesday at Detroit.
- Ordonez became the first Met with two sacrifice flies in one game since Alfonzo against San Francisco on Sept. 1, 1996.
- Ordonez ranged over from shortstop and made a diving stop to throw out Tino Martinez in the fourth on a grounder up the middle.
- Yankees C Joe Girardi was given the day off because of a stiff neck.
- Derek Jeter hit cleanup for the first time in his career and went 0-for-4. Williams moved up to No. 2.
- Orel Hershiser will try for his 200th career victory when he starts for the Mets on Sunday against Hideki Irabu.
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