Syracuse (4-0), making its first appearance in the tournament since winning it in 1998, plays its next game in Hawaii in a week against Minnesota.
The Orange closed the game on a 10-0 run, holding St. Francis scoreless for the final 4:10.
Syracuse's last nonconference home loss was to Cleveland State on Dec. 15, 2008. In that one, Cedric Jackson took an inbounds pass with 2.2 seconds left, turned and swished a two-handed, 60-foot shot at the buzzer to give the Vikings a shocking 72-69 victory over the 11th-ranked Orange.
The Orange were in trouble in this one until the final three minutes as its top scorer struggled mightily. C.J. Fair, who came in shooting 53.3 percent and averaging 21.7 points, couldn't buy a basket, going 2 of 13, all but one of his attempts coming from close range.
But with the game on the line and time winding down, the ball was in Fair's hands. He drove to the basket, missed at the rim and Grant was there to convert it to tie the game at 50-all. Grant then stole the ball and fed Gbinije for the decisive basket with 65 seconds left.
The Terriers (2-2) committed a turnover in the closing seconds and Ben Mockford threw up an airball 3 as the Orange escaped.
Dajuan Coleman matched his career high with 14 points and Trevor Cooney had 12 for Syracuse.
Jalen Cannon led St. Francis with 16 points and Anthony White had 10.
Ben Mockford broke a 46-all tie with a 3-pointer from the right corner at 4:48 coming off a timeout, but that was the last basket for the Terriers.
Moments later, Cooney missed a 3 from the top of the key and Tyler Ennis couldn't convert a drive through the lane as the Terriers held on to a 50-46 lead in a game in which neither team led by more than four points in the second half until the final minute.
St. Francis whooped it up before the game and in the runway before the second half, and that was understandable. The Terriers knocked off reigning Atlantic Coast Conference champion Miami 66-62 in overtime to open their season nine days ago. Cannon's layup with 1:02 left put St. Francis ahead for good as Miami never led in the extra session.
It was the first victory in school history against an ACC team, and the Terriers did it despite missing their first 13 shots of the game. They almost made it two in a row against the Orange, trailing just 30-26 at halftime and gained a 33-32 lead on White's 3, which came after a resounding block by Grant.
Coleman scored the Orange's first eight points and they reeled off 10 straight to take the lead after trailing in the first 3 minutes. Fair, who was 2 of 9 from the field in the opening 20 minutes, converted a rebound midway through the first half to give Syracuse an 18-10 lead, its biggest of the game.
A 3-pointer by Mockford and a three-point play by Cannon helped the Terriers close to 30-26 at halftime, the difference Cooney's four-point play for the Orange with 2:23 left.