Isaiah Williams' basket with 1:02 left gave Iona (24-6, 17-2 Metro Atlantic) a 73-65 lead and the Gaels made 6 of 8 free throws in the final minute.
Manhattan (15-13, 12-7) trailed 63-52 with 6:55 left but scored seven straight over the next three minutes to get within four on Ashton Pankey's three-point play.
Schadrac Casimir scored 15 points and Isaiah Williams added 12 for Iona, which won its 11th in a row. The Gaels entered the game having already clinched the regular-season title.
The Jaspers, who saw their three-game winning streak snapped, stayed tied with Monmouth for third place in the conference standings. Pankey scored 20, Emmy Andujar had 17 points and 10 rebounds, and Shane Richards added 14 points.