EAST RUTHERFORD, N.J. — Running back Jonas Gray scored a 1-yard touchdown early in the fourth quarter Sunday as the New England Patriots came back to edge the New York Jets, 17-16, at MetLife Stadium.

With the win, the Patriots (12-3) clinched a first-round bye. New England can clinch the No. 1 overall seed in the AFC by beating the Buffalo Bills next week.

Quarterback Tom Brady was 23 of 35 for 182 yards and a touchdown, a 3-yarder to tight end Rob Gronkowski. Wide receiver Danny Amendola had eight catches for 63 yards.

The Jets, likely playing at home for the final time under embattled head coach Rex Ryan, fell to 3-12.

Quarterback Geno Smith was 17 of 27 for 210 yards and a touchdown, a 20-yarder to tight end Jeff Cumberland. He also threw a key interception and took two costly sacks.

Gray’s touchdown run was set up by an interception by linebacker Jamie Collins, who picked off Smith at the Jets’ 40-yard line with 1:19 left in the third quarter.

The Jets had multiple chances to take the lead after Gray’s touchdown. New York drove to the New England 10 on its next possession, but Smith was sacked on second down and the Jets settled for Nick Folk’s third field goal with 7:57 left.

The Jets took over at the Patriots’ 30-yard line following an interception by cornerback Marcus Williams two plays into the Patriots’ next drive. But Smith again took a bad sack, this one for a loss of 10 on third down, and Folk’s 52-yard field-goal attempt with 5:21 left was partially blocked by defensive lineman Vince Wilfork.

The Patriots ran out the clock from there.

The Jets led 10-7 at the end of a first half in which they sacked Brady four times.

A 39-yard punt return by Amendola set up the Brady’s touchdown pass to Gronkowski with 12:14 left in the second quarter.

The Jets responded with an impressive 12-play, 87-yard drive capped by Smith’s touchdown pass to a wide-open Cumberland. Smith was 5 of 6 for 62 yards on the drive.

A 25-yard pass from Smith to wide receiver Percy Harvin set up kicker Nick Folk’s 26-yard field goal with 52 seconds left in the half.

Another short Folk field goal, this one a 23-yarder that ended a 66-yard drive, extended the Jets’ lead to 13-7 with 6:39 remaining in the third. The Patriots responded with a 13-play, 81-yard drive that kicker Stephen Gostkowski ended with a 24-yard field goal.

NOTES: Jets LB David Harris recorded the 1,000th tackle of his career when he and LB Calvin Pace teamed up to sack Patriots QB Tom Brady on New England’s first drive. Harris is the fourth player to record 1,000 tackles with the Jets. … Jets C Nick Mangold suffered an ankle injury and was carted off the field with 8:54 left in the second quarter. He has missed just two games since being drafted by the Jets in 2006. … The Jets also lost WR Percy Harvin to a rib injury in the third quarter. … Despite being listed as questionable on the injury report, Patriots CB Kyle Arrington (hamstring), RB LeGarrette Blount (shoulder) and WR Julian Edelman (concussion) were all inactive. … Brady took as many sacks in the first half as he did in the Patriots’ previous seven games combined.