Louisville (21-12) will play the winner of Thursday night's quarterfinal between Cincinnati and South Carolina next Tuesday at Madison Square Garden. Michigan and Old Dominion will play in the other semifinal.
Terrence Williams added 14 points for the Cardinals while Juan Palacios had a season-high 13 rebounds to go with eights points. Louisville held the Bears (22-9) to 27 percent shooting from the floor in winning its seventh straight home game.
Kellen Easley led Missouri State with 13 points but couldn't keep up with the Cardinals, who used a 22-4 run spanning the end of the first half and the beginning of the second half to take control.
After relying on Dean to keep them in the game early - he scored Louisville's first nine points and took 10 of its first 14 shots - his teammates picked up their play.
Andre McGee hit two 3-pointers and with Palacios single-handedly keeping Louisville competitive on the boards, the Cardinals responded in front of the largest crowd to see an NIT game this year.
Louisville built a 33-26 halftime lead by holding the Bears to one field goal over the final 7:15. The Cardinals shut down the lane and bottled up Missouri State guard Blake Ahearn, holding Missouri State's leading scorer to just six points on 2-of-11 shooting.
The win marked Louisville's deepest run in the NIT since 1985, when the Cardinals finished fourth.