The Hoyas (11-5, 3-2 Big East Conference) also got 11 points from Jabril Trawick and made 26 of 32 free throws.
Georgetown led 44-39 at halftime, but DePaul used a 14-5 second-half run to pull ahead 49-47.
The Hoyas, after the 12th lead change and 12th tie, made seven straight free throws and Smith-Rivera added a layup and jumper to lead 70-60 with 3:42 left. Simpson pulled the Blue Demons within 72-68 with a long 3 with 17 seconds left, but Smith-Rivera iced it.
Georgetown only made one field goal in the final four minutes, but went 8 of 12 from the line.