Brady threw a TD pass to Phillip Dorsett and Sony Michel ran for three scores to help the Patriots improve to 7-0 for the third time in franchise history, and first since 2015.
They also swept the two-game season series against their AFC East rivals for the fourth straight year, outscoring the Jets (1-5) 63-14 in the two meetings this year.
And, the top-ranked Patriots defense was a big reason in this one.
Darnold was the AFC offensive player of the week after leading New York to a 24-22 win over Dallas last Sunday in his return from missing three games with mononucleosis.
He was miserable against New England, finishing 11 of 32 for 86 yards and a 3.6 quarterback rating.