The Billikens (28-6) have won 16 of its last 17 games and never trailed in eliminating the New Mexico State Aggies (24-11).
St. Louis draws No. 12 Oregon, which ousted fifth-seeded Oklahoma State 68-55 in a Midwest Region second-round game later Thursday, in a third-round game Saturday.
The Billikens scored the first four points of the game and New Mexico State didn't get on the board until the game was 3 1/2 minutes old. St. Louis led by 13 at halftime.
While the Aggies pulled within 37-31, St. Louis soon regained a double-digit advantage and Cody Ellis had a 3-point shot and another jumper that put the Billikens ahead 49-34 with 9:36 to play.
Evans finished with 24 points on 11-of-16 shooting. Ellis had 12 points and Cory Remekun 11 for the Billikens. New Mexico State was led by Bandja Sy's 17-points.