Evans had 10 rebounds for the Billikens (8-1), who earned the 499th career victory for coach Rick Majerus. The 25th-year coach, who is in his fifth season at Saint Louis, goes for No. 500 against Illinois-Springfield on Saturday.
Luke Apfeld scored 13 points and Matt Glass 12 for Vermont (4-5).
Leading 34-27 at halftime, the Billikens went on a 13-2 run to start the second half to take permanent control. Evans scored five points during the surge, and Saint Louis eventually built the lead to 25 points.