Garrett, who was named Big East Rookie of the Year earlier in the day, tied for a team-high five rebounds for DePaul (12-20), which advances to face second-seed Creighton. Forrest Robinson tallied 14 points and Brandon Young chipped in 13 points.
D'Vauntes Smith-Rivera netted a game-high 21 points for Georgetown (17-14), which also got 17 points from Markel Starks.
A brutal first half ended with the Hoyas on top 25-23. Georgetown sank 38.5 percent from the floor in the period, which was a bit better than the 36 percent effort from the Blue Demons.
DePaul was able to push past the Hoyas after intermission by sinking 47.6 percent from the field and 13-of-17 at the free-throw line. Georgetown hit on 38.5 percent from the field once again to give up the lead and the decision.
Despite the loss, Georgetown had a 36-32 edge on the boards.