EAST RUTHERFORD, N.J. — Bill Parcells has never been crazy about kickers. Martin Gramatica may have changed the Dallas coach’s opinion. Gramatica, signed last Monday after Parcells cut the enigmatic Mike Vanderjagt, kicked a 46-yard field goal with a second left yesterday to give the Dallas Cowboys a 23–20 win over the Giants and a two-game lead in the NFC East.

“I’ve got to thank the Cowboys for giving me a second chance,” said Gramatica, once a top kicker who had just one field goal in three games since 2004.

“It’s been a rough couple of years for me,” the journeyman said, “being out all last year and then not making any teams this year.”

The winning score was set up by a 42-yard pass by Tony Romo to Jason Witten and came just over a minute after the Giants, wearing their red jerseys for the first and only time this season, had tied the game at 20-all on a 5-yard TD pass from Eli Manning to Plaxico Burress.

Gramatica, who also kicked field goals of 41 and 35 yards, was signed last week after the Cowboys cut Vanderjagt, who had received a three-year $5.3 million contract in the offseason.

But being the new guy didn’t keep Gramatica from bursting into one of his over-the-top celebrations: The diminutive kicker leaped into the arms of his teammates, while coach Bill Parcells broke into a wide smile on the sidelines as the ball sailed through.

“Gramatica made me look good,” Parcells said with a smile. “For a first game back in the league, you can’t get more pressure than that for the division lead.”

It didn’t look so good for Parcells on Gramatica’s first kick, a 44-yard attempt on the Cowboys’ opening drive. But the last kick, which went right down the middle with power to spare, more than made up for it.

“For a guy who hadn’t been kicking with regularity,” Giants coach Tom Coughlin said, “it was a difficult thing to do.”

It was the fourth straight loss for the Giants (6–6) and the fourth win in five games for Dallas (8–4) since Romo replaced Drew Bledsoe at quarterback at halftime of a 36-22 loss to New York on Oct. 23. He finished 20-of-34 for 257 yards with two interceptions.

“Anytime you come up to this place you know it’s not going to go smoothly,” Romo said. “We made mistakes today. I know I did. You just have to have a chance to do something at the end of the game to win.”

Both teams did — there were three scores in the final 3:33 — but the Cowboys had the last chance.

First, Marion Barber scored on a 1-yard run at the end of a 66-yard drive. Then Manning drove the Giants 63 yards for the tying score on the pass to Burress.

But Romo hit Witten on the first play after the kickoff with a strong throw to take the Cowboys to the Giants 26.

The Giants took an early 7-0 lead on their first possession, driving 66 yards on 10 plays with Manning hitting Jeremy Shockey on a 17-yard pass for the score. But they couldn’t score a touchdown again until the fourth quarter, despite first downs at the Dallas 4-yard-line twice in the second half – in each case, New York had to settle for field goals.

Dallas tied it at 7-all on Barber’s first plunge, which was set up by a bizarre sequence: Matthias Kiwanuka picked off a Romo pass and returned it 12 yards before he was stripped of the ball and Sam Hurd recovered for the Cowboys.

It was the second game in a row that the Giants’ rookie defensive end started to make a big play that turned into a mistake — last week he had Tennessee’s Vince Young in his arms for what could have been a game-winning fourth-down sack but released him because he thought Young had released the ball. Young then scampered for a first town and Tennessee went on to win.

Yesterday, the key sequence came just before the half.

With a fourth-and-short and 1:30 left, the Giants went for it, running short yardage specialist Brandon Jacobs outside, where he was stopped for a 3-yard loss. Romo then drove the Cowboys down the field for a 41-yard field goal by Gramatica.

In the second half, Gramatica and Jay Feely alternated field goals — the Giants kept getting closer than the Cowboys but couldn’t score a touchdown. Manning, who had been slumping lately, was 24-of-36 for 270 yards with two touchdowns and no interceptions.

The loss leaves the Giants, who were 6–2 at one point, with little margin for error if they want to make the playoffs — most likely as a wild-card entry.

“We have to approach it as if we have to win all four games,” Manning said. “Maybe three of four will get us in, but we can’t look at it that way. We have to approach it if we have to win them all.”