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.
Chad Ford and Jeff Goodman offer their opinions on the surprises they're expecting at the NBA draft, with Ford believing there will be a lot of trade activity while Goodman thinks people will be surprised by potential draft spot of Marquese Chriss.
Louisville coach Rick Pitino said he doesn't "have time to figure out what" Kentucky coach John Calipari meant in recent comments that appeared to be a jab at the Cardinals' program.
NC State lands guard Markell Johnson, who has reclassified into the class of 2016 after being ranked No. 48 in the ESPN 100 in the class of 2017.