Adrian Hilburn slipped a tackle and raced to a 30-yard touchdown catch with 1:13 remaining to pull Kansas State within two. Hilburn saluted the crowd behind the visitor's dugout and was flagged 15 yards for unsportsmanlike conduct, which pushed the 2-point conversion attempt back to the 17-yard line.
Carson Coffman overthrew Aubrey Quarles in the end zone, and when Kansas State (7-6) couldn't come up with the onside kick, Syracuse (8-5) only had to take a knee to win a bowl game for the first time since 2001.
Daniel Thomas ran for three touchdowns for Kansas State, which was making its first bowl appearance since 2006.
In a bowl season filled with blowouts so far, the first bowl game in New York in 48 years turned out to be a hit.
The teams traded big plays right from the start - Thomas went 51 yards for a score on the second play from scrimmage - and scored touchdowns on the first five second-half possessions.
Carter, who scored two second-half touchdowns, broke free for a 60-yard run on the next play. It set up Ross Krautman's 40-yard field goal with 3:08 left that made it 36-28.
Too much time.
Coffman, who played brilliantly in his last college game, led the Wildcats into Syracuse territory and connected with Hilburn near the sideline about 10 yards down field. After winning a footrace to the end zone, he dropped the ball, did a quick salute and turned to celebrate with his teammates.
The flags came flying and the 2-point attempt turned into a desperation play.
Coffman finished 17 for 23 for 228 yards and two touchdowns. Thomas was held to 90 yards on 22 carries by a defense that was geared to stopping him.
Ryan Nassib passed for 239 yards and hooked up with Sales on touchdowns of 52, 36 and 44 yards.
It was Big East against the Big 12 in the first bowl game in New York since the Gotham Bowl matched Nebraska and Miami at the original Yankee Stadium in 1962. The weather was pretty much as expected: cold.
But temperatures in the 30s were more than tolerable for the crowd of 38,274 - more than 44,000 tickets were sold, the Yankees said - especially considering 16 inches of snow got dumped on the city four days earlier. And the snow piled as much as 8 feet high next to the outfield walls and behind the end zone where home plate usually sits just added to the scenery.
Those who decided to brave the chill or make the long trip from the Little Apple (Manhattan, Kan.) to the Big Apple were rewarded with doozy of a game.
It was tied at 14 at the half, and Syracuse started the second attacking Kansas State's faulty run defense, which ranked 118th in the country after the regular season. Carter carried six times for 53 yards on a 60-yard touchdown drive, capping it with an easy 7-yard run that gave Syracuse a 21-14 lead.
Coffman marched Kansas State down with his running and passing to tie it at 21 with a 10-yard toss to Chris Harper in the back of the end zone.
Syracuse and Carter came right back with another long and steady march, this time capped by Carter with a 15-yard run. But Krautman knocked the point after wide and Syracuse led 27-21 heading into the fourth quarter.
And back came K-State. The Wildcats converted a fourth-and-2 from the Orange 9 with a 4-yard pass to Harper, then Thomas scored on fourth-and-goal from inside the 1, taking an option pitch around right end. The successful PAT made it 28-27 with 11:03 left in the fourth.
The fifth possession of the second half resulted in the fifth TD. Sales beat a fallen defender for a 44-yarder, but Syracuse's 2-point attempt failed and it was 33-28 Orange with 7:52 left.