After Paul White opened the overtime with a jumper to give Georgetown at 52-50 lead, Dunn had a three-point play and followed a two-miss possession by the Hoyas with a 3-pointer.
Dunn had a block on an attempted putback on the next possession and a Carson Desrosiers jumper put Providence ahead 58-52 with 2:01 to play.
Joshua Smith made three free throws on Georgetown's next two possessions and then L.J. Peak made a layup to Pull Georgetown within one. Dunn made two free throws with 10 seconds left before Tyler Harris' defense foiled Georgetown's last possession.
Dunn had nine assists and three steals for the Friars (13-4, 3-1 Big East).
D'Vauntes Smith-Rivera had 15 points and Smith 14 with 12 rebounds for the Hoyas (10-5, 2-2).