The win advanced the Hoyas (23-7) into the tournament quarterfinals against the fourth-seeded Cincinnati Bearcats. Pittsburgh fell to 17-16 on the season.
Connecticut, Louisville and South Florida also advanced to the quarterfinals. Connecticut, trying to win five Big East Tournament games in five days for the second year in a row, got past West Virginia in overtime 71-67 and will meet No. 2 Syracuse Thursday.
Louisville was a 61-55 winner over Seton Hall to set up a game against Marquette and South Florida ousted Villanova 56-47 to create a quarterfinal date with Notre Dame.
Pittsburgh led through the early stages of the game and was ahead 21-15 with 6:40 to go in the first half before Georgetown closed the period with a 16-2 run.
Porter started the run for a free throw and Sims capped it with a layup with 1:17 to go. Greg Whittington had a 3-point shot and a 3-point play in the spurt in which six Hoyas got on the board.
Louisville (23-9) held off a Seton Hall comeback thanks to Peyton Siva's 14 points. Seton Hall (20-12) shot only 32 percent from the field and made 3-of-19 from 3-point range.
South Florida got 17 points from Anthony Collins while improving to 20-12. The Bulls jumped to a 14-2 lead and never trailed. Villanova (13-19) was led by Mouphtaou Yarou with 20 points.
Sims, who also had 13 rebounds, and Porter combined for 14-of-21 shooting and Whittington wound up with 11 points for Georgetown. Ashton Gibbs had a team-high 14 points for Pittsburgh.
Connecticut (19-12) rallied from 11 points down in the second half against West Virginia (19-12).
It was the final Big East Tournament appearance for West Virginia, which joins the Big 12 next season.
Celebrity Families of 2014 [PHOTOS]