After a string of nine straight scoring sequences produced either a lead change or tie, Porter scored on a fast-break layup to make it 62-60 with 4:44 left to give the Hoyas the lead for good.
With Georgetown leading 62-61, the Hoyas came out of a timeout and got a critical three-point play from Porter off an entry pass from Starks to lead by four with 1:15 remaining.
Rutgers got a basket by from Carter with 55 seconds left before Porter hit both ends of a 1-and-1. The Knights missed two straight shots at the other end and Hopkins made two free throws with 14 seconds left put it out of reach.
After both teams shot well in the first half, Georgetown maintained its pace in the second while Rutgers cooled off.
Georgetown shot 57.4 percent overall (27 for 47) and hit 60.9 percent (27 for 47) in the second half. Rutgers shot just 38.9 percent (21 for 54) for the game and the Scarlet Knights were 10 for 33 (30.3 percent) after intermission.
Neither team could take control as the game featured 11 lead changes and four ties. The biggest lead by either side was seven points by Georgetown in the first half.
The first half, which ended in a 33-33 tie, was back and forth with each team pulling ahead before the other rallied back.
Trailing 13-7, Rutgers rallied to tie it 15-15 and 18-18 before Georgetown scored seven straight points for a 25-18 lead. With the score 27-21, Carter and Jerome Seagears hit 3-pointers to spark Rutgers to a 29-27 lead.
A foul shot by Judge to make it 33-33 forced the half's sixth tie to go along with four lead changes.
Starks and Smith-Rivera each had 12 points in the half while Starks was 3 for 4 from 3-point range. Carter had 14 points for Rutgers including three 3-pointers. Both teams shot well with Georgetown hitting 54.2 percent (13 for 24) and Rutgers shooting 52.4 percent (11 for 21).