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.
Mannion, who recently reclassified and is ESPN's No.11 overall player in the class of 2019, chose Arizona over Marquette.
He'll fit in with Sean Miller's plans for a faster tempo on offense.
The cream of the crop of American high school basketball will congregate in Colorado Springs from Oct. 5-7, as USA Basketball unveils its newly expanded Junior National Team minicamp in collaboration with the NBA, NCAA and NBPA.