St. Peter's led by two with 6:05 to go when it pulled away with 10 straight points for a 58-46 lead and 2:40 to play.
Trevis Wyche added 13 points and five assists for the Peacocks (7-14, 3-9 Metro Atlantic).
St. Peter's took control early by jumping ahead 19-12, but Ryan Oliver gave the Saints their first lead in almost 20 minutes at 33-31 on a layup with 14:47 left in the game.
The teams tied three more times before Dominique gave St. Peter's the lead for good at 43-40 on a dunk he converted for a three-point play with 8:44 to go.
Ryan Oliver led Siena (10-13, 6-6) with a career-high 15 points. Brett Bisping had 11 points and eight rebounds and Lavon Long scored 10.