The Irish finished 22 points below their average of 85.3, but held the Peacocks to 35.7 percent shooting from the field.
Bonzie Colson finished with 10 points and eight rebounds for Notre Dame.
Nick Griffin led Saint Peters (5-7) with 16 points.
Consecutive 3-pointers by Vasturia and Matt Farrell to open the second half helped Notre Dame extend its lead to 18 points. But the Irish missed their next 10 shots from deep, and Griffin's 3 with 5 minutes left cut the lead to nine points.
A flagrant foul on Travis Wyche with 4:05 left sent Notre Dame's Matt Farrell to the free throw line, but he missed the first one, snapping a streak of 31 consecutive makes for the Irish guard dating to last season.
Colson scored in the lane on the ensuing possession, pushing Notre Dame's lead back to 12 with 3:50 to play and they held on from there.
The biggest surprise of the first half came with 54 seconds left when Notre Dame guard Rex Pflueger committed his first turnover of the season, ending a run of 217 minutes without a miscue.
Saint Peter's: Already with two MAAC games in hand (1-1), the Peacocks closed out their non-conference slate against Notre Dame. Saint Peter's was picked to finish fourth in the conference.
Notre Dame: After finishing the first semester with a collective 3.1 GPA, the Irish have no school requirements for the next three weeks and can focus solely on basketball as they begin their ACC schedule.
Saint Peter's: The Peacocks return home for a MAAC matchup against league-leading Monmouth.
Notre Dame: The Irish kick off ACC play Saturday with their first true road game of the season at Pittsburgh.