Earnest Ross provided 16 points and seven rebounds for the Tigers (12-1), who wrapped up their non-conference schedule with an 8-0 home record. They begin SEC play Wednesday against Georgia in Columbia.
Missouri trailed 20-12 in the first half but then went on a 36-16 run to salt away the victory.
Jordan Clarkson added 11 points and Ryan Rosburg grabbed 11 rebounds to go with six points.
The 49ers (4-10) were led by Tyler Lamb's 17 points.
2014: The Year in Music [PHOTOS]