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.
Maryland point guard Melo Trimble, considered a lock to leave the program before struggling in the second half last season, has withdrawn from the NBA draft and will return for his junior season.
Louisville's Chinanu Onuaku, who recently underwent a medical procedure to correct a heart rhythm issue detected during the combine, will keep his name in the NBA draft pool.
Andrew White III will return to the Nebraska men's basketball team next season after removing his name from the NBA draft.