Vermont (1-2) used a 10-2 first-half run to make the score 33-23. Quinnipiac (0-2) later cut the deficit to five - 41-36 and 54-49 - but could get no closer.
The Catamounts shot 58.3 percent to 38.2 for Quinnipiac.
Giovanni McLean led the Bobcats with 18 points shooting 6 for 15 from the floor. He was 4 for 8 from 3-point range.
Nate Rohrer's dunk with 2:02 left gave Vermont its biggest lead to make it 77-60.
Quinnipiac had won three of its last four games against the Catamounts entering the game. Last year it handed Vermont its worst defeat of the season with an 89-73 win.
Vermont now owns a 7-3 series advantage against the Bobcats.