EAST RUTHERFORD, N.J. — Rex Ryan arrived as the head coach of the New York Jets in 2009 by declaring he was not intimidated by the New England Patriots or head coach Bill Belichick.

Ryan will likely depart the Jets next week feeling the same way the rest of the AFC East head coaching brethren has felt for most of the last 14 years: Closer than ever to dethroning the Patriots and farther away, all at the same time.

Running back Jonas Gray scored a one-yard touchdown early in the fourth quarter Sunday and defensive lineman Vince Wilfork blocked a field goal with 5:21 left as the Patriots hung on to edge the Jets 17-16 at MetLife Stadium.

“Another game I thought we had a helluva chance to win the game against New England,” Ryan said. “But that’s been the story four out of the last five times we’ve played them.”

It’s pretty much the story against everybody in the AFC East, which the Patriots have won in each of the last six years and 12 times in the last 14 seasons.

Of their 28 division wins since 2009, 10 have been by eight points or less. The Patriots have beaten the Jets by three points or less four times since 2012, including in the first meeting of this season on Oct. 16, when Jets kicker Nick Folk’s 56-yard field goal was blocked as time expired in New England’s 27-25 victory.

“I just wish we’d play better for 60 minutes — we just haven’t figured out a way to play against these guys as well as we possibly can,” said Patriots quarterback Tom Brady, who was 23-of-35 for 182 yards and a three-yard touchdown pass to tight end Rob Gronkowski. “Sometimes you’ve got to grind them out. Tough to win games in the NFL, certainly on the road against a division opponent.”

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

The Jets, meanwhile, fell to 3-12 in what is expected to be the home finale for Ryan, who will likely be fired following the season finale against the Miami Dolphins.

But it looked for much of Sunday as if Ryan might get to enjoy one last win over the Patriots. The Jets sacked Brady four times in the first half and took a 10-7 lead into the locker room.

As has been the case all season, though, the Jets ended up being done in by their sputtering offense.

What the Patriots said:

“We’ve played a lot of games like this against the Jets.” — Head coach Bill Belichick, regarding the fact that 16 of the 32 games between the Jets and Patriots since Belichick became the Patriots’ head coach have been decided by eight points or less.

What the Jets said:

“Every loss hurts. It does. This is a team that you think you have to beat going in. I didn’t think we’d have to beat them to get our fourth win of the season, but that’s where we’re at.” — Head coach Rex Ryan

What we learned about the Patriots:

1. The Patriots will be sitting home on wild card weekend watching teams beat each other up for the opportunity to face them — again. New England clinched its fifth straight first-round bye with Sunday’s 17-16 win over the Jets. But the Patriots still have plenty to play for: A win next Sunday against the Buffalo Bills will assure the Patriots home-field advantage throughout the AFC playoffs. The Patriots can also clinch home field if Denver loses to Cincinnati on Monday night. But even if that happens, expect Bill Belichick to approach the season finale as if it’s the Super Bowl. “Every game is important,” Belichick said. “You’re always playing for something.”

2. This is no news flash, but the reason the Patriots have become the dominant team during a salary-cap era intended to erase dominance is because nobody is better at doing the little things in every facet of the game. On defense, the Patriots minimized the damage during the Jets’ four trips inside the red zone by limiting New York to one touchdown and three field goals. The Patriots had just two sacks, but the first (a nine-yard takedown by defensive tackle Sealver Siliga) helped force the Jets to settle for a field goal down four in the fourth quarter. The second, a 10-yard sack by linebacker Dont’a Hightower, forced the Jets to try a go-ahead 52-yard field goal attempt — which defensive tackle Vince Wilfork blocked. After that, quarterback Tom Brady deftly ate up the final 5:16, during which he completed three passes to wide receiver Danny Amendola for 26 yards before third-string running back Brandon Bolden gained 17 yards on third-and-1 with 1:55 left. Add it all up and that’s how a 12-3 team beats a 3-12 team twice in a season by a total of three points.

–WR Julian Edelman (concussion) was inactive for the Patriots’ 17-16 win over the Jets on Sunday. Edelman was listed as questionable and as a limited participant in practice last week but didn’t even travel to New Jersey for the game. Edelman was injured in the Patriots’ 41-13 win over the Dolphins on Dec. 14.

–RB LeGarrette Blount (shoulder) was inactive for the Patriots’ 17-16 win over the Jets on Sunday. Blount was listed as questionable and as a limited participant in practice last week but didn’t even travel to New Jersey for the game. Blount has 219 rushing yards and three touchdowns since signing with the Patriots as a free agent on Nov. 20.

–DL Vince Wilfork blocked a 52-yard field goal attempt by Jets K Nick Folk to preserve the Patriots’ one-point lead in the fourth quarter of their 17-16 win on Sunday. The Patriots took over with 5:16 left and burned the remainder of the clock.

What we learned about the Jets:

1. Rex Ryan really wanted to go out with one more win over Bill Belichick and the Patriots. Sure, Ryan insisted after the 17-16 loss that he hadn’t given any thought to the possibility — or probability — that he was coaching the Jets for the final time at home, but his actions during the game and his demeanor afterward told how much he wanted to win and how much his ninth loss to Belichick stung. Ryan joined the group of Jets celebrating and jumping when cornerback Marcus Williams picked off Patriots quarterback Tom Brady to give the Jets — who were trailing by a point — the ball at the Patriots’ 30-yard line midway through the fourth quarter. Of course, quarterback Geno Smith got sacked on the third play of the subsequent “drive” and kicker Nick Folk missed a 52-yard field goal, which left Ryan despondent and sadly reflective afterward. Six years into his tenure as the Jets’ head coach — and one game away from the end of it — Ryan is no closer to knocking off Belichick than he was at the beginning. “They usually run away with our division,” Ryan said, “The one year we were both 9-2, we got smoked like a sausage in that Monday night game. That was probably the year we could have won the division.”

2. Whomever the new regime is for the Jets, it probably saw enough out of Geno Smith Sunday to know that he’s not going to develop into a franchise quarterback, or even a solid game manager. Smith’s lack of maturation isn’t his fault — he wasn’t ready to start as a rookie coming out of a spread offense at West Virginia — but the NFL is a win-now league and even a new head coach and/or new general manager will not want to hitch his/their wagon to a player whose progress has continually stalled out. Smith made three costly mistakes that cost the Jets at least 14 points on Sunday. His telegraphed a third-quarter interception — in which Patriots linebacker Jamie Collins made a leaping pick in front of tight end Jace Amaro — that led to New England’s game-winning touchdown. In the fourth quarter, Smith took two sacks, one of which forced the Jets to settle for a field goal when they were down four points and the other costing them 10 yards the play before kicker Nick Folk had a 52-yard field-goal attempt blocked. If Smith is going to develop into a serviceable starter, it’s almost certainly going to take place somewhere else.

–C Nick Mangold (left ankle) was carted off the field in the second quarter of the Jets’ 17-16 loss to the Patriots on Sunday. Mangold was injured when a Patriots player appeared to accidentally roll into him at the end of a 14-yard run out of the Wildcat by RB Bilal Powell. X-rays revealed no break, but Mangold, who was in a walking boot and on crutches after the game, said he will undergo more tests Monday. Mangold, who missed just five snaps all season before getting hurt, has played in all but two games as a pro since the Jets selected him in the first round of the 2006 draft.

–WR Percy Harvin (ribs) did not return after getting injured in the third quarter of the Jets’ 17-16 loss to the Patriots on Sunday. Head coach Rex Ryan had no update on Harvin following the game. Harvin had four catches for 44 yards, two rushes for 1 yard and a 19-yard kickoff return before getting hurt.

–QB Geno Smith struggled in the second half of the Jets’ 17-16 loss to the Patriots on Sunday. Smith oversaw an 87-yard touchdown drive in the second quarter that he ended with a 20-yard strike to a wide-open TE Jeff Cumberland. But the Patriots scored the game-winning touchdown early in the fourth quarter just eight plays after Smith was intercepted by Patriots LB Jamie Collins. Later in the fourth, Smith took two sacks, one of which forced the Jets to settle for a field goal and the other costing the Jets 10 yards the play before K Nick Folk had a 52-yard field goal attempt blocked. Smith finished 17-of-27 for 210 yards.