Albany (13-7, 8-0 American East) has won 11 of its past 12 games and has a two-game lead over Vermont (11-10, 6-2) for first place in the conference.
Vermont used a 10-3 surge, capped by Dre Wills' two-handed dunk, to tie it at 44 with 16 seconds left before Singletary hit the game-winner.
Singletary finished with 13 points. Sam Rowley had 18 points and Ray Sanders chipped in 10 points with 13 rebounds for the Great Danes.
Ethan O'Day scored 10 points to lead the Catamounts, and was the only Vermont player to reach double figures. Vermont scored a season-low 44 points while shooting 30.4 percent from the floor.