Trailing 19-15, the Catamounts (7-4) used a 15-4 run to lead by seven. The Knights answered with seven straight points, then pulled ahead 34-33 on Melquan Bolding's jumper at the horn.
In the second half, Fairleigh Dickinson (4-6) built a five-point lead at 44-39. A dunk by Ethan O'Day sparked a 13-2 Vermont run, with Apfeld capping the spurt with a 3-pointer.
After the Knights got within four with 10:40 left, the Catamounts pushed the lead into double figures for good.
Voelkel had 10 points, 10 rebounds and eight assists for Vermont, which has won three of its last four games.
Clancy Rugg added 13 points off the bench for the Catamounts, who outscored Fairleigh Dickinson's reserves 21-0.
Bolding led the Knights with 20 points.
Indiana guard James Blackmon Jr., who averaged 15.8 points in 13 games before being injured last season, has withdrawn from the NBA draft.
Isaiah Briscoe has decided to withdraw from the NBA draft and will return to Kentucky for his sophomore season. Marcus Lee intends to transfer.
The Big 12/SEC Challenge will again feature Kansas and Kentucky, this time at Rupp Arena. That's not the only exciting matchup in next season's midseason conference showdown.