It is the second successive season the Orange (16-0, 3-0 Big East) have opened with 16 victories in a row. Last season's team went 18-0 before its first loss.
Scoop Jardine added 10 points and 11 assists for Syracuse.
Gerard Coleman and Vincent Council each scored 17 points for Providence, and LaDontae Henton had 11 points and 13 rebounds. The Friars (11-5, 0-3) were playing the No. 1 team in the nation for the first time since beating top-ranked Pittsburgh 81-73 in Providence in 2009.
Providence took its last lead of the game when Council was fouled making a 3-pointer with 1:46 left in the first half. He made the free throw to give the Friars a 34-33 lead, but Triche hit a 3-pointer to give Syracuse a 36-34 halftime lead.
It was 40-38 with two minutes gone in the second half when the Orange scored nine straight points. After Brice Kofane made one of two free throws, Triche hit another 3-pointer and then added another that made it 55-41 with 15 minutes left.
Henton hit a 3-pointer to make it 62-55 with just under 10 minutes left, but he missed two free throws that could have cut it to five points after being fouled on a fourth-chance put-back. Triche drove for a layup, then Council was called for a charge; James Southerland made a 3-pointer to give Syracuse a 67-55 lead.
Providence made it a six-point game, 70-64 with 5:33 left, but never got any closer.
Providence honored Dave Gavitt during its first conference home game since the death of the former Friars coach, Big East commissioner and Naismith Hall of Famer. There was a moment of silence for Gavitt, who died on Sept. 16, and a halftime video tribute.
Earlier in the day, the city renamed a street near the arena "Dave Gavitt Way." The Friars had previously named their court for him, and they are wearing "DG" patches on their jerseys this season.