Rodgers, playing at MetLife Stadium for the first time since breaking his Achilles tendon in his debut last season, tossed two touchdown passes to snap an eight-game home losing run against their AFC East rivals.
He found Allen Lazard from 10 yards to put the Jets ahead in the first quarter, and Breece Hall doubled the lead from one yard out.
Joey Slye opened the scoring for the Patriots with a 44-yard field goal before halftime, but that was the best the visitors could do.
Rodgers threw a second touchdown pass to Garrett Wilson in the third quarter, and a Greg Zuerlein field goal finished the scoring after the Jets recovered a fumble.
Rodgers finished with 281 yards, while his counterpart Jacoby Brissett had a disastrous night as the Patriots managed only four first downs in the first half.
Brissett was sacked five times and threw for only 98 yards before being replaced by Drake Maye, the third overall draft pick, late in the fourth quarter.
