The Orange improved to 14-0 overall by using Joseph's scoring ability, Jackson's rebounding dominance and Scoop Jardine's -- who netted 21 and dished out seven assists -- point-guard presence.
Syracuse (1-0 Big East), which entered the game going undefeated during its non-conference schedule for the second straight season, led 42-23 at halftime.
However, Providence (11-3) and senior guard Marshon Brooks, who also scored 27, battled and fought back from a 14-2, second-half run by the Orange to make it a close late in the game.
Leading 51-47, Syracuse rallied to gain a 65-49 advantage with 9:12 remaining.
The Friars (11-3) inched their way back using 3-point baskets by Gerard Coleman and Brooks that capped a small spurt that closed the gap to five points, 70-65, with 3:30 to go.
Providence got to within four points after Coleman hit a 2-point jumper with 3:08 remaining, but the Friars never got any closer because SU closed out the game by going six of eight at the free-throw line.
On Saturday, Syracuse hosts No. 15 Notre Dame (3:30 p.m. on ESPNU). The Fighting Irish host their conference opener Wednesday night against No. 9 Georgetown Hoyas.
On Wednesday morning, check out full recap and breakdown of Tuesday night's college hoops action at SB Nation New York.