EAST RUTHERFORD, N.J. — With one mighty heave, Tom Brady and Randy Moss took care of the record books. Now it’s down to business for the unbeaten New England Patriots: stamping themselves as the greatest team in NFL history.

The Patriots completed a perfect if somewhat joyless journey through the regular season tonight, finishing with a remarkable 16-0 record following a thrilling 38-35 comeback victory over the New York Giants.

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 comeback from a 12-point deficit engineered by the brilliant Brady, and smashed the Patriots’ league mark for consecutive victories.

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

In gaining their 19th straight win over two seasons, the Patriots also got record-setting performances from Brady and Moss, including the winning score, a 65-yard bomb with 11:06 remaining. Brady beat Peyton Manning’s mark of 49 touchdown passes by throwing two to Moss against the Giants (10-6), giving the star quarterback 50. 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.

Yet this was anything but a coronation. The Giants, with little to play for except spoiling New England’s perfect ride — New York is guaranteed playing at Tampa Bay in the playoffs next weekend — 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.

An efficient Eli Manning, at times resembling his vaunted older brother, threw for four touchdowns. 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 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.

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 from early in the season, well, 19-0 would speak pretty loudly.

Patriots coach Bill Belichick hugged players and assistant coaches on the sideline as the game ended.