St. Joe's has only two seniors on the roster, but one of them, guard Charoy Bentley, made one of the game's biggest shots when he drained a three-pointer with 1:15 remaining for a 72-63 lead.
The Hawks were up, 50-40, after a fastbreak layup by Justin Crosgile when Rutgers began to methodically cut into the deficit, eventually pulling within 64-63.
But Jones nailed a pair of free throws and followed them by streaking down the lane for a layup to push the lead back to five points.
The Hawks were coming off their best half of play in the young season. In Tuesday's 60-51 win over Fairfield, St. Joe's shot a blistering 68.2 percent (15 for 22) and held the Stags to 26 points over the final 20 minutes.
St. Joe's picked up where it left off in Bridgeport, Conn., as Galloway played a smooth floor game that belied his inexperience, leading the Hawks to a 34-28 halftime lead. The native of Baton Rouge, La., and nephew of St. Joe's assistant coach Geoff Arnold, Galloway started a 12-0 run with a pair of free throws after Rutgers' Robert Lumpkins was called for a technical foul for hanging on the rim too long after his dunk.
After the technical on Lumpkins, the Scarlet Knights went 5:18 without scoring and the Hawks turned a one-point deficit into a 33-22 lead with 12 consecutive points, seven from Galloway. Jones scored the other five points. Rutgers closed the half with three-point jumpers by Austin Carroll and James Beatty.
Rutgers coach Mike Rice was an assistant at St. Joseph's for two seasons - 2004-05 and '05-06.