Shane Southwell put Kansas State ahead and then swatted away any chance of a West Virginia triumph.
Southwell finished with 17 points and hit a pair of go-ahead free throws with 21.4 seconds remaining in the 18th-ranked Wildcats' 65-64 win over the Mountaineers.
On West Virginia's ensuing trip down the floor following Southwell's foul shots, Jabarie Hinds missed a jumper with 12 seconds left, but the ball went out of bounds and back to the Mountaineers.
Kansas State's Angel Rodriguez knocked the inbounds pass away and into the backcourt. With the clock ticking down, a scrambling Gary Browne retrieved the ball and frantically drove the lane, but met Southwell, who emphatically blocked the shot away with a second remaining.
"We fought too hard for that game," Southwell said. "We just needed to find a way to win."
Rodney McGruder added 17 points for Kansas State (13-2, 2-0 Big 12), which has won six straight.
Hinds netted 15 points to lead the Mountaineers (8-7, 1-2), who have dropped eight in a row against top-25 foes.
West Virginia again played without second-leading scorer Juwan Staten, who was benched for a second straight game for disciplinary reasons.
"He has to get on the same page as me or he is not going to play anymore," Huggins said.
The back-and-forth affair was played within a one-possession window over the final 13:20 after two Aaric Murray free throws pulled the Mountaineers within 48-45.
Later, Rodriguez's right baseline jumper gave Kansas State a 63-60 lead with 2:14 left before a Murray jumper a little over a minute later made it a one- point game with 1:21 to play.
After McGruder misfired from the right elbow, Eron Harris drove on Will Spradling along the right baseline before pulling up and nailing the jumper for a 64-63 Kansas State edge with 25 ticks to go.
The Wildcats took a 36-33 cushion into the halftime break.
Murray tallied 11 points and five rebounds ... Kansas State shot 51 percent (25-of-49) from the field, while West Virginia shot 51.1 percent (24-of-47) from the floor.