With rain pouring down as it had been throughout the second half, New England's Aqib Talib intercepted a pass by Geno Smith at the Jets' 46 with 48 seconds remaining to seal the victory.
Talib also intercepted Smith early in the fourth period after the Jets had moved within range of a field goal that would have tied the game.
Brady drove the Patriots 81 yards in six plays the first time they had the ball and hit Aaron Dobson with a 39-yard scoring pass that put New England in front for good.
The New England quarterback became only the second in NFL history to throw at least one scoring pass in 50 consecutive games. Drew Brees of the New Orleans Saints holds the all-time record of 54 straight games with a TD throw, a streak that came to an end last season.
Stephen Gostowski added field goals of 21 yards in the first period and 30 yards in the second to help give the Patriots a 13-3 halftime lead and the defense then put the clamps on Smith and the Jets.
Brady completed 19-of-39 passes for 185 yards without an interception in pacing the Patriots to their second win in as many games to start the season. It was New England's 12th straight win over a division rival.
Smith, starting his second game as a professional, went 15-of-33 for 214 yards. The Jets fell to 1-1.
The Jets outgained the Patriots 318 yards to 232 and had the ball for eight more minutes than did New England. New York, however, turned the ball over four times overall.