Painter led all scorers in the first half with 10 points to help Old Dominion (1-0) take a 28-27 lead into halftime.
The Monarchs pulled away in the second half, outscoring the Bears (0-1) 34-24 in the second period.
Painter was one of six players that scored in double digits for Old Dominion.
Nick Wright and Keenan Palmore each scored 12 points for the Monarchs, while Aaron Bacote, Donte Hill and Dimitri Batten added 10 points apiece.
Old Dominion shot the ball better in the second half, converting on 54.2 percent (13 of 24) of its shots compared to Morgan State converting on just 41.9 percent (13 for 31).
Justin Black led Morgan State with 16 points, while Dewayne Jackson and Anthony Hubbard scored 13 points apiece.