The Hoyas trailed by seven with 2 minutes left in the second extra period, but produced their second late rally of the contest and came up with the winning basket when Porter drove through three defenders for the layup.
Georgetown stayed in front by itself in the Big East Conference race with its 10th straight win, one that came after the Hoyas had come from 12 points behind inside the 5-minute mark of regulation.
The Hoyas' Omar Calhoun forced overtime by hitting a 3-pointer with 2.2 seconds to go in the second half.
Connecticut's Ryan Boatright missed a shot at the buzzer at the end of the first extra session and his desperation attempt to close out the second overtime also misfired.
Porter scored 22 to lead Georgetown (22-4, 12-3 Big East) and Markel Starks had 15. DeAndre Daniels had 25 points for Connecticut (19-8, 9-6).