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.