Darryl Bryant added 15 points and Gary Browne 13 for the Mountaineers (9-2).
Caleb Patterson led the Bears (7-4) with 18 points.
Trailing 63-60 late in regulation, Browne hit a fall-away 3-pointer with 1.6 seconds left to force overtime. It was Browne's only 3-pointer of the game.
West Virginia had rallied from a five-point deficit with 45 seconds left in regulation.
Trailing by two with 2 seconds left in overtime, Missouri State's Nathan Scheer put up a shot in the lane, but it bounced around the rim and out.
Both teams have one game left in the Classic. West Virginia plays No. 6 Baylor on Friday, while Missouri State plays Saint Mary's.