The Peacocks moved out to a 47-38 lead with 9:13 remaining as Dominique hit a layup and a jumper, but Marist rallied late.
Adam Kemp made a layup and Khallid Hart followed with a steal, leading to two free throws to make it 57-56 with 16 seconds left.
Trevis Wyche split a pair of free throws for Saint Peter's, and T.J. Curry was then sent to the line with 3 seconds left. Curry made the first, but missed the second and Jay Bowie's putback couldn't find the net as time expired.
Saint Peter's (10-16, 6-11 Metro Atlantic Athletic Conference) shot 44 percent from the field and hit 9 of 19 3-pointers.
Hart led the Red Foxes (11-16, 8-9) with 15 points and Bowie had 12 with 10 boards.