Southwell's free throws with 21.4 seconds remaining put the Jayhawks (13-2, 2-0 Big Ten) ahead for good, and his block of Gary Browne's try for a game-winning lay-up as time was expiring preserved the victory.
Southwell finished with 17 points while Rodney McGruder also provided 17 as the Wildcats won their sixth straight.
Jabarie Hinds paced the Mountaineers (8-7, 1-2) with 15 points.
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