It looked to me like the Patriots let the Giants score, to get the ball back with more time on the clock.
They did. One object of the play, from the Giants' point of view was to NOT score. That's strange in its own right, but that was the strategy (and it was a good one). I can't recall any other game where the team in possession was "going" for a TD, but didn't want it - then made it (accidently), even though it was not what they wanted.
Very memorable play.
That didn’t work for Holmgren against the Broncos and it didn’t work for Belichek against the Giants.