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EAST RUTHERFORD, N.J. (AP) -- Tom Brady was as giddy as the quarterback of an unbeaten and perhaps unbeatable team should be. Had Bill Belichick spotted him slapping the backs of his New England teammates, the dour coach might have scoffed.

After all, a perfect 16-0 regular season won't mean much if the Patriots don't win their next three games and another Super Bowl.

"We've been dealing with being undefeated all season," Brady said Saturday night after the thrilling 38-35 victory over the New York Giants in a game worthy of the NFL's championship showcase. "It was kind of a strange game. It really doesn't mean much to either team, but it means a lot."

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New England became the first NFL team since the 1972 Dolphins to win every game on the schedule, and that one was only 14-0. This victory required a Brady-engineered comeback from a 12-point deficit and smashed the Patriots' league mark for consecutive victories.

"Going undefeated during the regular season is a remarkable achievement," 1972 Dolphins coach Don Shula said. "I know firsthand how difficult it is to win every game, and just as we did in 1972, the Patriots have done a great job concentrating on each week's opponent and not letting any other distractions interrupt that focus. If they go on to complete an undefeated season, I will be the first to congratulate Coach Belichick and the Patriot organization."

Validation of the Patriots' inexorable march through the season can only come by adding a Super Bowl championship. Do that, and there'll be no challenge to their spot at the top.

"Hats off to us," said record-setting receiver Randy Moss, who caught Brady's 65-yard bomb for the go-ahead score that set two major records. "I know a lot of people didn't think we were going to do it. A lot of people didn't want us to do it.

"In this game of football, it's hard to go 16-and-0. As a football player and a fan of the game, my hat's off to this organization."

In gaining their 19th straight win over two seasons, the Patriots went on top on Brady's 50th touchdown pass of the year and Moss' 23rd TD reception. It came with 11:06 remaining.

Brady beat Peyton Manning's mark of 49 touchdown passes and Moss broke Jerry Rice's record of 22 TD receptions. And the Patriots finished with an incredible 589 points for the season, another single-season record.

Once the victory was clinched, Belichick was barely more animated than usual. He shared hugs with players and assistant coaches on the sideline, but there was no thought of carrying him off on the Patriots' shoulders or dumping Gatorade all over him.

That will have to wait for three more wins -- if they come.

"It's a great feeling," Belichick admitted. "Now is the time to take a day or two and appreciate what this team has done, but at the same time we have our biggest game of the year coming up. Pretty soon we need to turn the page and move on."

Who knows, the Patriots might even find the Giants on one of the next pages, especially if Eli Manning again resembles his vaunted older brother.

"We didn't win the game, but if you saw everybody in the locker room, everybody was excited," Manning said. "I never saw a locker room so upbeat after a loss because we played so well, did some good things and hung in there in a game where we didn't have to play. We wanted to. We wanted to come out and play well, and we did that."

The Giants (10-6), already guaranteed a playoff game against Tampa Bay next weekend and with little to play for except spoiling New England's perfect ride, led 28-16 in the third quarter. It was the Patriots' largest deficit all year as the Giants showed no fear and plenty of versatility, scoring the most points New England allowed in a game during this remarkable run.

Manning threw for four touchdowns and Domenik Hixon, in his first game as New York's primary kick returner, went 74 yards for a score 11 seconds after Brady and Moss tied their respective records.

Not to worry. These Patriots are unflappable, and they matched their comebacks in wins over Dallas, Indianapolis, Philadelphia and Baltimore earlier in the season. A 73-yard drive ended with Laurence Maroney's 6-yard run to make it 28-23 with 4:00 to go in the third period.

Then came the most familiar of scenes: Brady dropping back, winding up and hitting a wide-open Moss in stride for a touchdown. The final go-ahead TD in their perfect year.

"What I'm most proud of is playing a playoff team on the road that was playing extremely hard," Brady said. "We found a way to come back and win. We did the same thing at Dallas. We did the same thing at Indy. We've been in some tough games.

"Everyone is going to enjoy this one. It happens once every 35 years."

Although many are eager to hail these Patriots as the NFL's all-time best, such acclaim won't come unless they win two playoff games and their fourth Super Bowl this decade. And for those who might deny such greatness considering the "Spygate" scandal, well, 19-0 would speak pretty loudly.

Certainly louder than any postgame celebrations at Giants Stadium, the same building where they were caught videotaping New York Jets assistant coaches in Week 1, a rules violation that cost Belichick and the franchise $750,000 in fines and a 2008 first-round draft choice. That made Belichick even more close-mouthed and dour than usual, and his team followed his lead -- right to 16-0.

The Giants opened the game as if they were, well, the Patriots, driving 74 yards, sparked by a 52-yard completion on which Plaxico Burress outleapt Ellis Hobbs for Manning's jump-ball throw. Brandon Jacobs broke Tedy Bruschi's tackle to score on a 7-yard reception for a 7-0 lead.

Naturally, the Patriots, the highest-scoring team in NFL history, struck back. After Stephen Gostkowski's 37-yard field goal, New England went on top -- and surpassed Minnesota's league mark of 556 points -- on the record-tying 4-yard TD pass from Brady to Moss, who soared above rookie Aaron Ross for the score.

The 10-7 lead lasted all of 11 seconds. The usually staid Patriots gathered around Moss as he did a dance in the end zone, prompting a 15-yard excessive celebration penalty. Belichick argued the call with referee Mike Carey, perhaps sensing how costly it might be.

It was as Hixon sped 74 yards untouched to lift the Giants back in front.

"There is nothing but positives," Giants coach Tom Coughlin said. "I told the players in playing this game everything would be positives, there would be no negatives and that is how I feel.

"I don't know any better way to be prepared for the playoffs than to go against a team that was 15-0."

Gostkowski kicked two more field goals as the Patriots grabbed a 16-14 lead with 1:59 left in the half.

That's when Manning, coming off several rough games, was at his best, leading a quick 85-yard drive that included a rare scramble for 11 yards just before he found Kevin Boss in the middle of the end zone with 13 seconds remaining. The 21-16 deficit was only the second time New England has trailed at halftime this season; the other was to the older Manning and the Colts.

But with such a potent offense, the Patriots never are out of any game. Once they got the lead, they closed it out with another touchdown drive, Maroney scoring from the 5. Manning hit Burress again from 3 yards with 1:04 to go, but New England recovered the onside kick.

"We're down 10 or 11 (actually 12) in the third quarter, the crowd was into it, and we found a way to win," Brady said. "That's the way it's going to be down the stretch ... just hope we can continue to play this kind of football."

Game notes

Brady finished 32-for-42 for 356 yards, while Manning was 22-for-32 for 251 yards and the only interception. ... The other teams to go unbeaten in a season were the 1934 and 1942 Chicago Bears; both lost in the NFL title game. ... New England also set a league mark with 75 touchdowns. ... The Giants lost center Shaun O'Hara, backup safety Craig Dahl and linebacker Kawika Mitchell, all with knee injuries, and cornerback Sam Madison with an abdominal strain.