Peters was 9 of 13 from the field, hit 9 of 10 from the free-throw line and grabbed six rebounds for Valparaiso (4-1). The Crusaders made 53.3 percent of their shots, including 12 of 21 from behind the arc.
Shaun Lawton led Maine (0-4) with 16 and Kevin Little had 15. Aaron Calixte and Marko Pirovic added 10 apiece for the Black Bears.
Peters scored eight points during Valparaiso's 17-2 run to start the game. He had 15 points through the first 8 minutes and finished with 22 points in the first half. Valparaiso went on to lead 52-28 at halftime after shooting 61.3 percent from the field.
Tevonn Walker hit two free throws with 12:13 left to give Valparaiso a 33-point lead, its largest of the game.