Siena (17-10) never trailed. The Saints, from the Metro Atlantic Athletic Conference, went on a 12-0 run to take a 21-9 lead with 5:10 gone.
Boise State (20-7) narrowed its deficit to 45-40 at halftime and pulled to within 48-46 two minutes into the second half on a basket by Matt Nelson, who finished with 20 points.
Led by Kenny Hasbrouck, who wound up with 19 points, and Ubiles, the Saints then pulled steadily ahead, finishing the game on a 13-5 run.
Siena held Boise State's leading scorer, Reggie Larry, to only eight points, 10 below his season's average.
The smaller Saints outrebounded the Western Athletic Conference Broncos 44-36 and outscored Boise State 46-28 in the key. Siena used its quickness to force 20 turnovers, while committing only nine themselves.