The Hoyas handed the Cardinals their first loss of the season in the opening Big East Conference game for both teams.
Louisville had opened the season with 12 straight victories. Georgetown (11-1) has won nine in a row since losing to Kansas.
Georgetown owned a 63-52 advantage with 4:27 left to play but the Cardinals ran off 11 in a row and tied it with 2:01 left on a layup by Gorgui Dieng.
Henry Sims then missed a layup for the Hoyas, but Porter was there to tip in the offensive rebound that put Georgetown in front for good. Sims hit two free throws 31 seconds later and Porter made two more foul shots with 40 second remaining for a 69-63 Georgetown lead.
Markel Starks scored 20 points for Georgetown while hitting 7-of-8 shots from the field. Porter came off the bench to score 14 points and grab 14 rebounds.
Louisville was led by Kyle Kuric with 17 points and Peyton Siva with 15.