This time, the defensive tackle didn't commit a penalty as he did last season on Folk's failed 56-yard try in overtime that gave the kicker another chance - a 42-yarder that gave the Jets a 30-27 win.
''It was so fitting that he made that play'' Thursday, Belichick said. ''That was awesome.''
Danny Amendola hasn't lived up to the $28.5 million, five-year contract he signed before last season but caught a 19-yard touchdown pass - just his fifth reception this season - that gave the Patriots a 27-19 lead.
''Nobody works harder than Danny,'' Belichick said. ''He's a really competitive kid, tough.''
That the outcome wasn't decided until the final play was a surprise.
The Jets hadn't won since their opener and Geno Smith was last in passer rating in the NFL. But he completed 20 of 34 passes for 226 yards, one touchdown and no interceptions.
''We can take a lot of positives from this,'' New York wide receiver Eric Decker said, ''but at this point we need a win, period.''
The Jets (1-6) dropped their sixth straight game, the longest losing streak in Rex Ryan's six years as coach.
''We're not going to sit here and sulk about losing the games because that's going to make things worse,'' Smith said.
The Patriots (5-2) have a 1 1/2-game lead in the AFC East over Buffalo.
''We started off the year 0-1 so 5-1 since is not bad,'' said Tom Brady, who threw three touchdown passes and has nine with no interceptions in his last three games. ''Hopefully, we can be a lot better.''
Some more things to know from the Patriots' win:
TOP KICKERS: Folk's miss, two yards further than the longest field goal of his career, was his first of the season after making 13 straight.
''It felt pretty good off my foot,'' he said. ''I did kick it low, in order to give it enough to get it there.''
Stephen Gostkowski made both his field-goal attempts for the Patriots and is 18 for 19 this season.
WASTING TIME: The Jets had a nearly 2-to-1 advantage in time of possession, 40:54 to 19:06, and ran 80 plays to 53 for the Patriots. But New York settled for four field goals by Folk when they got inside the Patriots 30-yard line on each of their first four possessions.
''We had a couple of big penalties in the red zone that hurt us,'' Ryan said. ''It looks like we are good enough to win and then we make too many mistakes.''
RUSHING ADVANTAGE: The Jets also had a big advantage in the ground game, running 43 times for 218 yards compared to 15 carries for 63 yards for the Patriots, who lost Stevan Ridley for the season last Sunday with a knee injury.
Chris Ivory led New York with 107 yards on 21 carries and a 1-yard touchdown run that gave them a 19-17 lead six minutes into the fourth quarter.
''The offensive line did a great job pushing those guys back and giving us lanes to run,'' Ivory said.
Patriots defensive tackle Vince Wilfork expected the Jets to rely on the running attack.
''You run the ball 30 or 40 times, you are going to have a little success,'' he said.
BRADY'S TOUCHDOWNS: Brady completed two touchdown passes to Shane Vereen, a 49-yarder far behind the secondary on the Patriots' fourth offensive play and a 3-yarder. Then he connected with Amendola for the 19-yard score with 7:49 left.
''That was a great kind of ad lib,'' Brady said of the Amendola play. ''He ran a little return route and then when he saw me scramble (he) broke it up field like we talk about all the time and he made a great catch.''
TIME TO REST: The Patriots wasted little time getting on a roll with three wins in 12 days after a 41-14 loss to the Kansas City Chiefs. Now they have the weekend off before preparing for the second of three straight home games, against the Chicago Bears.
''We're ready for a little break,'' safety Devin McCourty said. ''We can go into this long weekend and be happy.''
None of New York's next seven opponents has a winning record.
NOTES: Brady has won 41 consecutive regular-season home games against AFC teams. ... Jets rookie TE Jace Amaro was held to three catches after getting 10 against Denver. ... Patriots CB Darrelle Revis had two tackles and one pass defensed against his former team.
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