Manhattan led by as many as 10 points in the second half, but had to hold off a late charge by the Gaels.
English cut the deficit to two points twice down the stretch, with a layup and uncontested dunk with 18 seconds to play.
Iona then fouled Donovan Kates, who made one of two free throws for his only point of the game. That set up the last try by Laury.
Iona, which averages more than 10 3-pointers per game, went 6 for 21 from long range against the Jaspers.
Manhattan led by eight early in the second half, but Iona responded by scoring the next 11 points, highlighted by Isaiah Williams' big dunk after he grabbed the rebound of a Laury miss.
Manhattan came right back. C.J. Jones' dunk capped a 9-0 run that put the Jaspers back on top 44-38, and they never gave the lead back.
Whenever Iona would get close, Shane Richards would hit a 3-pointer. His third of the half made it 59-54, and sparked an 8-0 run that put the Jaspers up by 10 points with 6 minutes to play.
Iona was looking for its third straight trip to the NCAA tournament. The Gaels, who got an at-large bid two years ago, are not expecting one this season.
"If you look at what we did in the last 20-25 games of the year, then we're an NCAA team," coach Tim Cluess said. "If you look at our overall record, we're probably not. Our job was to win tonight. We didn't."
The New York rivals, whose campuses are less than 10 miles apart, were playing for the 85th time. They split their games in the regular season.
The two losses to Manhattan are the only two the Gaels have had in their last 16 games.