Lavon Long scored a team-high 17 points for Siena (17-17), which will await its semifinal-round opponent once the tournament is re-bracketed.
Brett Bisping tallied 12 points and 12 rebounds for the hosts, while Rob Poole added 11 points and eight boards.
For PSU (16-18), D.J. Newbill was the lone player in double figures, but scored 17 points despite his 5-of-18 shooting from the field.
Siena ended the first half on a 5-0 surge to take a 25-21 lead at intermission. The Saints shot just 36 percent from the field in the low-scoring opening half, while the Nittany Lions were even worse at a meager 28.6 percent shooting.
After the Saints extended their lead to as many as seven with under 14 minutes to play, the Nittany Lions used a 13-3 run to take a 41-38 advantage with 8:25 left on a Geno Thorpe dunk.
The sides exchanges a few more leads down the stretch until, with Siena leading by two with 10 seconds left, Brandon Taylor tied the game with a layup for PSU.
The Saints responded on the other end with Hymes' clutch bucket, and Newbill's 3-point attempt in the waning seconds was off the mark.
Not only did PSU have an awful field goal shooting night (.298), but it also shot a lackluster 12-of-22 at the free-throw line.