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EAST RUTHERFORD, N.J. (AP) -- Mike Nugent was already hugging Ben Graham, thinking he had just won the game for the New York Jets.

He didn't see the yellow penalty flag sitting on the wet turf a few yards away.

"Ben kind of whispered to me and said, 'Hey, there's a flag, so don't get too excited yet,'" Nugent said.

Moments after having a 33-yard field goal negated by a penalty, Nugent kicked a 43-yarder 5:13 into the extra period to give the Jets a 13-10 victory over the Kansas City Chiefs on Sunday.

"Things like that can happen," Nugent said. "The guys did a good job of making sure it didn't happen on the next one."

With both offenses struggling and a freezing rain falling throughout, not even the return of Chiefs coach Herman Edwards to Giants Stadium could spice up this one. Edwards coached the Jets from 2001-05 and led them to the playoffs three times.

The stadium was only about half full when the game started, and Edwards didn't receive much of a reception -- positive or negative -- when he and his Chiefs took the field. He was booed early in the game when he went out to talk to the officials about challenging a play that couldn't be challenged, and again when he called timeouts to try to ice Nugent before each of his kicks in overtime.

"It's kind of fitting to go overtime," Edwards said. "It's two teams both having disappointing seasons."

Nugent made the 33-yarder that appeared to win it, but Wade Smith was called for holding and pushed the Jets (4-12) back 10 yards, hardly an easy kick given the wet conditions.

"Oh, man, I was already throwing my gloves in the crowd," running back Leon Washington said, shaking his head.

After Edwards called a timeout, Nugent coolly sliced the uprights to give the Jets the victory.

"The guy we have here, he hasn't missed any when it comes down to it, so I had faith in him and I knew he would get it done," Washington said.

The Jets ran out to midfield to congratulate Nugent while the remaining fans cheered wildly. The victory sent the Jets off on a positive note after so much was expected following a 10-6 season and a playoff appearance in coach Eric Mangini's rookie campaign.

"It's been a tough season, obviously," running back Thomas Jones said. "The one thing I can take from this year and this team is that a lot of guys fought hard and we all stuck together."

The loss was the ninth straight for the Chiefs (4-12), who had tied it at 10 with just under three minutes remaining in regulation. One of the few bright spots for Kansas City was Tony Gonzalez, who broke Shannon Sharpe's NFL record for catches by a tight end.

"We're underachievers," said Gonzalez, who has 820 career receptions. "It's embarrassing. It's frustrating. I think it's ridiculous. We're one of the worst teams in the NFL, record-wise. That's something I never thought would happen out here in Kansas City."

Jones finished with 98 yards on 25 carries and caught a 15-yard touchdown pass from Kellen Clemens, who started for the Jets after missing last week with a rib injury. Clemens was 13-of-25 for 115 yards.

Kansas City tied it at 10 with 2:59 remaining when Brodie Croyle found Jeff Webb in the back of the end zone for a 26-yard touchdown. Croyle, who missed most of Kansas City's game last week at Detroit when he bruised his throwing hand, was 20-of-43 for 195 yards.

"Am I glad it's over? Yeah," Edwards said. "Now we can go to try and improve our football team."

The Jets took a 7-0 lead 1:53 into the second quarter on Jones' 15-yard reception off a shovel pass from Clemens, the running back's first TD catch this season.

The drive was helped by a little trickery. With New York facing a third-and-3 from Kansas City's 44, Washington took a direct snap, rolled to his right and hit a wide-open Wallace Wright for a 36-yard gain.

"It's something we had worked on in practice all year," Washington said. "Coach Mangini told me I had the power of choice, so I wanted to throw the ball and I tried to back-shoulder him."

On third-and-goal from the 15, Clemens took the snap and the pocket collapsed quickly, but he tossed to Jones, who zigged to his left and then zagged to his right before getting into the end zone.

Kansas City's John Carney kicked a 40-yard field goal with 5:08 left in the first half to make it 7-3. Nugent kicked a 27-yard field goal with 13 seconds remaining in the half to give the Jets a seven-point lead.

Game notes

Jets special teams coach Mike Westhoff announced after the game he won't return next season. He needs surgery on his ailing leg, which has had previous operations to treat bone cancer, and will require extensive recovery time. Westhoff wouldn't say he's retired, though. ... Chiefs running back Kolby Smith left after injuring an ankle during Kansas City's first possession. Rookie free agent Jackie Battle replaced him and had 44 yards on 13 carries.