The Catamounts (10-3, 1-0 America East Conference) trailed 43-42 with 6:03 left to play, but a 3-pointer from Brendan Bald and jumpers from Joey Accaoui, Voelkel and Fjeld gave Vermont a 51-45 lead with 1:20 remaining.
Stony Brook (6-7, 1-1) led 28-21 with 1:24 left before halftime, but the Catamounts scored the final five points of the half to enter the break trailing 28-26.
Marcus Rouse led all scorers with 19 and was the only player in double figures for the Seawolves.
Vermont went 10 for 21 from the floor (47.6 percent) in the second half and struggled from 3-point range, going 1 for 13 (7.7 percent) for the game.
Stony Brook shot just 20.7 percent after halftime (6 of 29) and made just one field goal over the final 4:31.
Florida State's student government has passed a resolution discouraging Seminoles fans from wearing Native American headdresses at games.
The second annual Gavitt Tipoff Games, eight games between members of the Big East and Big Ten to be played Nov. 14-18, will feature Villanova at Purdue in the opener.
Michael Lewis is leaving his assistant coaching job at Butler to take the same position at Nebraska under Tim Miles.