Judge was a perfect 9-of-9 from the field.
Myles Mack added 19 points, four rebounds and four assists for the 11th-seeded Scarlett Knights (15-15), who advanced to play sixth-seeded Notre Dame in Wednesday's second round.
Jerome Seagears added 15 points and seven boards as Rutgers broke open a close contest in the second half, outscoring Blue Demons 44-26.
Cleveland Melvin pumped in 25 points and Brandon Young added 15 for DePaul No. 14 DePaul (11-21).
In Tuesday's other first-round game, Fuquan Edwin lifted 12th-seeded Seton Hall over South Florida 46-42 on a pair of free throws with 0.9 seconds remaining in overtime.
The key foul shots gave Edwin 17 points as the Pirates (15-17) advanced to take on fifth-seeded Syracuse.
Eugene Teague helped out with 14 points and 10 rebounds in the victory.
Zach LeDay led the 13th-seeded Bulls (12-19) with 13 points, 15 rebounds, five blocked shots and three steals.