Freshman guard Four McGlynn scored 18 points and 59, in the first round of the 2012 NCAA Tournament.
Matt Glass and Sandro Carissimo added 11 and 10 points, respectively, for the Catamounts (24-11), who will face North Carolina, the Midwest Region's top- seed, on Friday.
Vermont, which captured the America East Conference title, has won 15 of its last 16 games. The Catamounts claimed their second NCAA Tournament victory in school history.
"I think that a lot of people underestimate the position that we were in as a First Four team, but for us it was a great honor," McGlynn said. "We won our conference championship and got an automatic bid. And, I mean, it's really good. It just allows us to continue our season. And fortunately we got a win today to keep our season going."
Devon Lamb ended with 16 points and six rebounds for the Cardinals (23-12), who made their first appearance in the NCAA Tournament since the 1999-2000 season. Mike James had 16 points and Anthony Miles tallied 14 in defeat.
Vermont took control of the game near the midway mark of the first half. Trailing by three, 12-9, the Catamounts put together a 13-0 run. McGlynn tallied five points during the burst, including a jumper with 8 1/2 minutes left for a 22-12 margin.
James' slam and Donley Minor's three-pointer cut the gap to five, but Vermont answered with an 8-2 flurry. Glass' layup made it a 30-19 game with two minutes to go.
Miles made a pair of free throws to cut the gap to nine at the break.
The Catamounts, though, maintained control in the second half, starting the frame on an 11-4 run. Glass' three-point play extended Vermont's lead to 41-25 with 16:51 to play.
Lamar, which won the Southland Conference title game, never got closer than eight the rest of the way.
"I mean, like you said, shots didn't fall," Lamar head coach Pat Knight said. "I don't know if it was because we were a little timid or what it is. But second half we finally relaxed. We started off hot, but I don't know, just a couple of bad plays and we just couldn't get it going. So that hurt us going down the stretch."
Wednesday's bout marked the first-ever meeting between these two schools on the hardwood...James fouled out with 4:42 to play...Vermont shot 50 percent from the floor, while Lamar shot 33.3 percent...The Catamounts got 35 points from their bench, compared to just five for the Cardinals...Stan Brown had six points and 13 rebounds for Lamar.