Redshirt-sophomore Ka-Deidre Simmons (Newark, N.J.) also finished in double figures for the Pirates, scoring 11 of her 13 points in the second half in addition to racking up eight assists, the second highest single-game total in her career.
Simmons also stretched her double-digit scoring streak to 10-straight game and tied her career-high with two three-point field goals.
As a team the Pirates tied their single-season high with nine three-pointers while attempting a season-high 30 long-range shots.
Seton Hall (7-11, 2-3) started off hot from three-point range, with Green hitting her first two attempts of the game, and the Pirates grabbed an early 13-11 lead when senior Brittany Morris (Raleigh, N.C.) converted from outside for her first bucket.
Georgetown (11-7, 2-3) applied a lot of pressure around the perimeter on Simmons and the Pirates did not find many offensive chances in the paint through 20 minutes of action, taking 16 three-pointers in the first half and sinking six of them.
Andrea White powered the Georgetown attack early on, making five of her first six field goal attempts while giving the Hoyas an 18-15 lead on a mid-range jump shot with 8:19 left in the first half.
After a six minute field goal drought the Pirates heated back up from outside as Green buried her third triple with six and a half minutes remaining the first, followed by Morris 90 seconds later and then it was Green once again, sinking her fourth three of the period to give Seton Hall a 24-22 lead with fewer than four minutes left in the first.
Seton Hall limited Georgetown senior guard Sugar Rodgers, who entered Saturday's game leading the nation in scoring with 24.6 points per game, for much of the first half as she missed her first three shots and picked up a second foul with 7:51 left in the opening period.
But Rodgers went on a tear to end the first, scoring all eight of her points of the half over the final two and a half minutes, including a three pointer with a minute remaining that helped Georgetown take a 32-28 lead into the locker room.
Green led all scorers in the first with 14 points on 4-for-9 shooting from three. While Simmons only scored two first-half points, she did a great job finding Seton Hall's open outside shooters, finishing with six assists in 18 minutes of action.
Simmons found some offensive rhythm very quickly in the second half, knocking down an outside shot on Seton Hall's first possession and then hitting a 10-foot jumper 30 seconds later to pull her team within one, 32-31.
The Pirates were still down by just one point after the Hoyas failed to get back on defense following a missed shot, leading to Simmons finding junior Janee Johnson (Matthews, N.C.) for a wide open fast-break layup on the other end with 13:55 still to play, to make the score 36-35.
Georgetown answered that score with a 16-0 run over the next four and a half minutes to take a 17-point lead which it never relinquished.
Rodgers led Georgetown with 24 points on 9-for-20 shooting to go along with 10 rebounds and seven assists, while White finished with 18 points and eight rebounds Brittany Horne scored 15 points.
Seton Hall begins a two-game home stand when it hosts the USF Bulls on Tuesday, Jan. 22, in Walsh Gymnasium at 7 p.m.