EAST RUTHERFORD, N.J. -- Aldrick Rosas delivered the game-winning 23-yard field goal to give the New York Giants a thrilling 12-9 overtime victory over the Kansas City Chiefs on Sunday at MetLife Stadium.

The Giants took a 6-3 halftime lead. They also tried some rare trickery on their first drive, which included a fake punt that saw running back Shane Vereen's pass intended for tight end Evan Engram picked off by safety Daniel Sorensen.

After the Chiefs failed to convert on the Giants' turnover, New York defensive tackle Damon Harrison picked off Kansas City quarterback Alex Smith's shovel pass intended for tight end Travis Kelce at the Chiefs' 26-yard line.

Smith, who has run a similar play before, was asked if he thought the Giants knew the shovel pass was coming.

"I don't think they knew," he said. "They made a nice play on it looking back on it, but I'm not sure they knew what was coming."

The Giants then marched 26 yards on six plays toward a 1-yard touchdown run by running back Orleans Darkwa to take a 6-0 lead. Rosas missed the extra point.

The Chiefs got on the board in the second quarter with a 31-yard field goal by Harrison Butker to cap a 15-play, 61-yard scoring drive that chewed 9:17 off the clock, cutting the Giants' lead to 6-3 at the half.

The Giants took the lead in the fourth quarter when cornerback Janoris Jenkins picked off Smith deep in Kansas City territory. Rosas atoned for his missed extra point earlier in the game by hitting a 26-yard field goal with 1:41 left in regulation to give the Chiefs the 9-6 lead.

The Chiefs got two fourth-quarter field goals from Butker, including a game-tying 26-yarder that came with one second remaining to send the game into overtime.

However, they struggled to get much else going on offense, as Smith, who finished 27 of 40 for 230 yards and no touchdowns, struggled to get into a rhythm.

"Does he have a couple of throws he would like to have back? Yes, I think he would," said Chiefs head coach Andy Reid. "This is all part of everyone being part of that. It's not just Alex there as you look at it. We all have a piece of that thing."

New York's winning drive in overtime was set up thanks to a 36-yard reception by receiver Roger Lewis, who also drew a pass interference penalty on Chiefs cornerback Phillip Gaines before Rosas' game-winning field goal.

Rosas, who had missed a field goal in five of his last games in which he attempted a three-pointer, said he was determined to overcome the windy conditions throughout the game and snap his slump.

"Coming out, we knew this game was going to be windy, so I really prepared to be mentally strong," he said. "I mean, that's every kicker's biggest nightmare when it starts to get a little windy, but if you stay true to your form and hit a nice ball, it will cut straight through the wind."

The Giants snapped a three-game losing streak in their first home win of the season.

"It's great to get a win at home," said head coach Ben McAdoo. "We fought through a lot of adversity, played heavy handed and physical. Just a tremendous team win ... against a good football team."

Reid, whose Chiefs started 5-0 only to go 1-4 ever since, didn't sound like he was ready to panic just yet.

"It's tough to win in the National Football League," he said. "There is parity. It doesn't matter if you are 1-8 or whatever it might be. There is opportunity. You have to bring your A-game every week and we have to get ourselves back to playing better. It's my responsibility to do that."

The Chiefs (6-4) will host Buffalo next week. The Giants (2-8) head to Washington to face the Redskins on Thanksgiving night.

NOTES: This was the first time since Sept. 10, 1995, that the Giants and Chiefs went into overtime. That game ended in a 23-20 Chiefs win. ... With the loss, the Chiefs' nine-game road-game win streak that began in Week 6 of the 2016 season (at Oakland, Oct. 16, 2016) ended. ... The Giants are undefeated at home against the Chiefs. ... Giants QB Eli Manning moved into sole possession of second place for most consecutive regular-season starts (209), passing brother Peyton, whom he tied last week. Manning also needs five more games to match Hall of Fame DE Michael Strahan's franchise record of 216 games played in a Giants uniform. ... Chiefs K Harrison Butker's three field goals gave him 22 straight conversions, the fifth-longest streak in franchise history.