West Virginia battled for most of the game, but Kansas dominated in the paint and pulled away from the Mountaineers to win, 83-69.
Staten had 22 points to lead the Mountaineers.
The Jayhawks won the rebounding battle (37-28), and more than doubled WVU's points in the paints, led by Andrew Wiggins (19 points), Wayne Selden (17 points) and Joel Embiid (11 points, 10 rebounds).
West Virginia started off hot, with Harris making deep threes and Staten getting to the hoop. The two teams battled back and forth in the first half, and WVU even had a 30-27 lead with 6:26 left in first half.
However, the Mountaineers did not make a field goal over the final 7:55 in the first half, and Kansas began to take control, getting ahead by as many as nine points. Much of that came from the duo of Selden and Wiggins, culminating in a last-second putback dunk by Wiggins, putting the Jayhawks ahead 43-36 at the break.
West Virginia did not give up, though, battling back after the break, cutting the lead back to two, 46-44, after a three-pointer from Nathan Adrian. Kansas' dominance underneath returned, however, and the Jayhawks extended the lead back up to twelve, 68-56.
West Virginia's shooting woes returned, though, with the Mountaineers not making a field goal for over five minutes, and Kansas pulled away after that.
West Virginia (14-10, 6-5) has a quick turnaround, returning to Morgantown tonight for a matchup against Iowa State on Monday evening. The game is set for a 7:00PM ET tip in the WVU Coliseum and will be televised nationally on ESPNU.