Presbyterian's Armel TeTe made a layup to open the scoring in overtime but the Blue Hose (11-18, 4-12) went 0 for 6 from the field, missed their only free-throw attempt from there and Radford closed on an 8-0 run.
Davon Bell hit a 3-pointer to give Presbyterian a 66-65 lead with 13 seconds left in regulation but Phillips hit 1-of-2 free throws with a second left to force overtime.
Senior Ruben Arroyo, who came in averaging 3.4 points per game, hit five 3-pointers and finished with 17 points -- both career highs -- for the Blue Hose. Bell added 16 points and six assists.
Duke leapfrogs Kansas for No. 1 in latest AP Top 25 poll
Duke has supplanted Kansas atop the new AP Top 25 poll after its dominating win against Kentucky, giving the Blue Devils a record number of appearances at No. 1.
Seminoles make Week 1 statement
Duke grabbed most of the Week 1 headlines, but the Noles made a statement of their own.
Simmons, Duffy help North Texas beat Hawaii 68-51
Jahmiah Simmons and Jorden Duffy scored 13 points apiece to help North Texas beat Hawaii 68-51 on Sunday night.