After Fairfield cut Iona's 41-30 halftime lead to 47-46 with 13:25 remaining, a three-point play by Jones began a 14-4 run by the Gaels (12-6, 6-1) that included 3-pointers by Armand, DaShawn Gomez and Jones.
Jones scored 22 of his points in the second half and had all 13 of Iona's points in one stretch.
Derek Needham did his best to keep the Stags (10-9, 2-5) in the hunt, scoring 19 of his 26 points in the second half, including five 3-pointers, but they lost their fourth in a row.
David Laury had 14 rebounds for Iona, which is tied with Niagara atop the conference standings.
The Gaels made 21 of 31 free throws to Fairfield's 9 of 13.
Former Kentucky guard Ed Davender, the only Wildcat with at least 1,500 points and 400 assists, has died. He was 49.
Guard Naz Mitrou-Long, whose 2015-16 season ended in December due to hip problems, has been granted a hardship waiver for the coming season, Iowa State said.
As the Sooners look to life without superstar Buddy Hield and his sidekicks, it's clear their unseasoned players will need to grow up fast.