Matt Stainbrook scored 20 points, Dee Davis added 17 and sixth-seeded Xavier beat No. 11
Stainbrook took advantage of his size in the post, making 8 of 10 shots in the paint and adding nine rebounds and five assists.
Davis was nearly as good from the outside, hitting four of nine shots from three-point range. Coach Chris Mack pulled them to a rousing ovation with 1:51 remaining and the game in hand.
Xavier (22-13) advanced to face 14th-seeded Georgia State on Saturday.
Xavier's inside-out duo was considerably better than Mississippi's two-man guard tandem. Stefan Moody and Jarvis Summers finished a combined five of 26 from the field. Moody led the Rebels (21-13) with 14 points.