Bucknell led throughout the second half but the Great Danes kept pressing until Wheeler Baker slipped in for a layup to close the gap to 59-58 with 1:46 left.
Albany's Evan Singletary missed a 3 with 22 seconds left. Ryan Frazier then made two free throws for the final score. Baker missed a 3-point attempt with six seconds left. Nana Foulland grabbed the rebound and was fouled, but missed both shots, giving Albany one last chance with 2.6 seconds remaining. Peter Hooley's heave from midcourt missed as time expired.
Foulland had 12 points for Bucknell (4-6).
Both teams were hot from beyond the arc as Bucknell made 7 of 18 and Albany nailed 6 of 15.
Sam Rowley had 17 and Singletary added 15 for Albany (2-6).