Manhattan led 38-37 at intermission after a first half that produced seven lead changes and nine ties.
Pepperdine gained its only lead in the second half at 44-42 after Rico Tucker completed a three-point play with 16:58 left.
Freshman Chris Smith, playing in his first game after sitting out the first semester, hit a 3-point shot to cap a 15-3 run for Manhattan and propel the Jaspers to a 57-47 lead with 12:08 to go.
The Waves tied the game at 64 when Shelley scored with 6:13 remaining, but never went ahead.
Ferguson's free throw with six seconds left gave Manhattan an 80-76 lead.
Shelley made a 3-pointer for Pepperdine at the buzzer.
The Jaspers were 7-for-17 from 3-point range. The Waves were 3-for-11 on 3s.