Seventh-seeded Missouri State (17-15) will face second-seeded Illinois State (22-8) in a quarterfinal game at 6 p.m. Friday.
The Bears have won four in a row and five of their last six. Tenth-seeded Evansville (9-21) finishes with a losing record for the eighth season in a row, a school record.
Kavon Lacey led Evansville with 13 points.
Dex Manswell and Shane Laurie had 10 points each for the Bears.
Missouri State, coming off back-to-back 22-win seasons, used a 14-0 run in the first half to take control 26-11. Evansville battled back with consecutive 3-pointers from Shy Ely and Darin Granger, but Chris Cooks halted the rally with a 3-pointer for Missouri State.
The Bears, who led 35-24 at half, scored the first 13 points of the second half to put the game away early. Evansville missed its first 11 shots in the second half and went 7:35 without scoring.
Mitchell sank his first four shots from the field and scored 10 of his team's first 22 points. He also pulled down seven rebounds.
Missouri State beat Evansville 76-38 during a regular-season meeting Feb. 16 in Springfield.
The Bears, who went 8-10 in league play, received their lowest seed since 2001, when they also were seeded seventh.
Evansville, under first-year coach and former Purple Aces standout Marty Simmons, lost five of its final six games.
It's going to take a minor miracle for Missouri State to match the 22 wins the Bears had each of the past two seasons. But don't look now, they've won four in a row to get to 17.
Next up, after Thursday night's rout of Evansville in the opening round of the Missouri Valley Conference tournament, the seventh-seeded Bears will meet No. 2 Illinois State in the quarterfinals.
Missouri State, coming out of its lowest seed in this tournament since the 2001 team was also at No. 7, hopes the old adage about how tough it is to beat a team three times in a season holds true Friday night.
The Bears lost by a point to Illinois State at home on Feb. 2, and they fell by 12 on the road 11 days later.
- Jay (The Real MSU)