Armond Battle added 13 points for the sixth-seeded Raiders (19-13), who will play third-seeded Cleveland State in the second round on Friday in Milwaukee.
Wright State won all three games against Wisconsin-Green Bay (14-18) this season.
The Raiders led 50-48 with 3:04 left before Battle and Duggins keyed a 10-0 run for a 60-48 lead with 39 seconds left. Battle scored five points and Duggins had a three-point play in the outburst.
Cooper Land added 11 points and N'Gai Evans had 10 for Wright State, which won despite shooting 36.2 percent from the field (17 of 47).
Alec Brown scored 15 points, Jarvis Williams had 10 points and Daniel Turner had 12 rebounds for the Phoenix, who had 18 turnovers.