Luke Devlin added 12 points and Jacob Iati converted a pair of clutch 3-point shots late in the game to give the Great Danes (24-10) their third trip to the NCAAs.
Iati, who finished with eight points, did not attempt a shot until the closing minutes. His first 3-pointer in the home stretch gave Albany the lead for good with 2:36 left in regulation.
Trey Blue and Clancy Rugg led Vermont (21-11) with 10 points apiece. The Catamounts (21-11) were the defending conference champs.