Dee Davis made four 3-pointers en route to 17 points for the sixth-seeded Musketeers (22-13), who are making their ninth NCAA Tournament appearance in 10 years. Xavier will play 14th-seeded Georgia State on Saturday.
The Panthers stunned third-seeded Baylor earlier Thursday in a West Region matchup.
Stefan Moody ended with 14 points for the 11th-seeded Rebels (21-13), who rallied past BYU in Tuesday's first round. M.J. Rhett and Ladarius White tallied 12 and 11 points, respectively.
The Musketeers started the game on a 16-5 spurt and never looked back. After Ole Miss got within 21-17, Stainbrook recorded a three-point play to spark a 15-4 Xavier run.
Remy Abell capped the burst with a jumper to make it 36-21. The Rebels, who erased a 17-point halftime deficit to defeat BYU, scored the final three points of the first half to get within 36-24.
Rhett opened the second half with a jumper, but Xavier scored the next seven points.
Davis' 3-pointer gave the Musketeers a 43-26 lead with 17:54 to play. The Rebels never got closer than 10 the rest of the way.
Game Notes: The Musketeers are one of 11 teams that have made the NCAA Tournament in nine of the last 10 years ... Xavier shot 46.4 percent from the field and went 10- of-23 from beyond the arc.