Consider the seasons of the two Super Bowl contestants.
Giants were 6-2 then went on their 4 game losing streak, losing to 49ers, Eagles, Saints and then the Packers. They got a little juice going in their game against the Packers, gave some signs that maybe the worst was behind them and were still breathing, one game behind the Cowboys in the division. Then they went down to Dallas and beat the Cowboys, bringing their record to 7-6 and putting them in control of their playoff fate. The next week they suffered a truly dispiriting loss to an awful Redskins team, dropping the Giants to 7-7 and giving the fans the sorry feeling that the win against the Cowboys was an illusion. Next up was the Jets. The stadium coresidents, the trash talking, we're the big brother in town, we're going to the Super Bowl Jets. Giants playoff run began in earnest. They had to win the last two games of the year to make the playoffs and the Jets stood in their way. Giants beat the Jets, then in succession beat the Cowboys, Falcons, Packers and 49ers. So once they met the Jets, they have not lost another game in the season.
Now let's look at the Patriots season. Patriots were nearly perfect in the first 6 games of the season going 5-1 with their only loss an upset by the Bills. Then they had a bad loss to the Steelers and an even worse loss to the Giants. Two game losing streak and a 5-3 record with the Jets coming up in a road game for them at Met Life Stadium. Jets were licking their chops to avenge an earlier season loss on the road and smelled a wounded animal in the Patriots on a two game losing streak. Patriots crushed the Jets 37-16 and have not lost since.
There you go --- the two Super Bowl contestants, both considered bitter rivals of the Jets, have not lost a game since playing the Jets. Too bad Giants didn't play them earlier in the season.