It was the Tigers ninth straight NIT victory at home. But this one did not come easily.
Syracuse (24-11) cut Clemson's 17-point lead to 69-68 on Demetris Nichols' tip-in with 19.8 seconds left. However, Rivers, the team's best free-throw shooter, hit a pair of foul shots to extend the lead.
Josh Wright's open 3-pointer with about 10 seconds left bounced off the rim and into the arms of Tiger guard Vern Hamilton.
Hamilton followed with two foul shots to clinch the victory - and Clemson's first trip to Madison Square Garden since 1999.
Then, the Tigers (24-10) were second to champ California. This time, they can keep a curious streak alive for the Palmetto State as they try and become the third straight South Carolina team - the Gamecocks won the past two NITs - to hold the trophy.
AIR FORCE ACADEMY, Colo. - Jacob Burtschi scored 13 points, including the winning basket with 7.7 seconds left to send Air Force to the NIT semifinals.
Draelon Burns, who scored 18 points and had five 3-pointers, rimmed out a 3-pointer from the right corner at the buzzer after Burtschi missed a free throw following his layup, and the usually subdued crowd at Clune Arena stormed the court, their Falcons headed to the NIT Final Four and "New York, New York" playing over the loud speakers.
The Falcons (26-8), top seeded in the West, play South Region top seed Clemson in the semifinals on Tuesday night at Madison Square Garden in New York. Mississippi State will face West Virginia in the other semifinal.