The Gaels (8-6, 2-1), who trailed 38-28 early in the second half, were still behind by nine with 9:14 left before rattling off 11 straight points to lead 51-49. Sean Armand’s 3-pointer started the run, then Jones scored five straight points and Armand capped it with another trey.
The lead changed eight more times, with Iona scoring six straight points to lead 63-58 with 21 seconds left.
The Saints (2-12, 0-3) closed the gap to three twice, but got no closer, with the Gaels making 3 of 4 free throws.
Armand added 14 points, David Laury 12 and A.J. English 11 for Iona.
O.D. Anosike had 19 points and 15 rebounds, while Rob Poole added 18 points for Siena, which has lost 10 straight.