Evan Turner missed a leaner from 15 feet that would have forced a third OT for the Buckeyes (22-11), who blew an 11-point lead in the second half of regulation.
Siena came into the tournament with a higher profile for a small school after shocking Vanderbilt in the first round last March. The little college from upstate New York returned a veteran squad that was given a solid chance of beating one of the Big Ten's powers.
Siena pulled it off despite playing much more like sinners than Saints.
Siena committed 22 turnovers and made just 6-of-23 3-pointers, but Moore, who was 0-for-4 from 3-point range in regulation, drained his two big shots when it mattered most.
Once the final horn sounded and Siena had moved on for a date with the fearsome Cardinals, coach Fran McCaffery wrapped his arms in around his point guard and carried him off the floor as the Saints fans, outnumbered by the thousands, chanted "Ron-ald Moore."
The Buckeyes had everything going their way. They were playing just an hour from home and they had the size, strength and stature on their side.
It didn't matter to the Saints, champions of the Metro Atlantic Athletic Conference, who stormed from behind in the second half.
Ryan Rossiter scored 16 points with 15 rebounds for Siena, which relied on its tournament experience from last year's run to pull it through.
The young Buckeyes, who don't have a senior on their roster, went up 72-71 when Turner, who had 25 points, nine rebounds and eight assists, knifed through the lane for a layup with 17.9 seconds left. But Moore, a rocket with the ball in his hands, calmly lined up from the right wing and buried his second clutch 3.
Ohio State will remember this as a game that got away.
The Buckeyes led 41-30 after Turner made a 3 with 14:31 left and OSU had a chance to possibly put the Saints away when sharpshooter Jon Diebler lined up for a 3 from the corner. His shot caromed long and it gave Siena a reprieve it wouldn't waste.