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.
Kansas State coach Bill Snyder, sensing field goals would not be enough, called for a fake with about five minutes left in the fourth from the 10, but Syracuse stacked up Ryan Doerr on the run.
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.