West Virginia (4-7, 2-6) needed to win out vs. the bottom of the conference to make it to a bowl. But, that wasn't possible, as Kansas (3-7, 1-6) had the Mountaineers' number in front of a small crowd at Memorial Stadium.
WVU has now lost five of its last six games heading into a bye before it takes on Iowa State at home on Nov. 30.
Since the Mountaineers beat Texas a year ago, WVU is 6-13 and 4-11 in the Big 12.
Sims was spectacular against a usually gritty WVU rush defense. Sims finished with 211 yards and three touchdowns on 22 carries to lead the Jayhawks.
Cozart was 5-of-12 for 61 yards and also had 60 yards rushing.
Without starting quarterback Clint Trickett, who was on the sidelines in street clothes due to a concussion he suffered last week vs. Texas, Paul Millard struggled. He was 23-of-42 for 242 yards and two touchdowns but had a very costly interception early in the second half and another in the fourth quarter.
Despite the wind that limited both teams' offenses, WVU didn't stick with the run as many expected. Starting running back Charles Sims had just 16 carries for 99 yards.
WVU finished with 386 total yards. Kansas had 376 yards - 315 of those coming on the ground.
Outside of the first drive of the game where West Virginia drove 75 yards in six plays and scored a touchdown, the Mountaineers were basically unsuccessful on offense until late in the game.
Kansas took a 10-7 lead in the second quarter on a touchdown run from Sims, and it was a lead the lowly Jayhawks would never relinquish.
Following another WVU punt, Sims broke open through a gaping hole and ran untouched 68 yards to the end zone to take a 17-7 lead at the half.
A field goal attempt by kicker Josh Lambert was blocked at the end of the half.
Kansas opened up the second half by going three-and-out and then just a 10-yard punt. However, Millard made a giant mistake near field goal range, as he threw a pass right to Kansas linebacker Ben Goodman. He returned the interception 54 yards to the WVU 14-yard line. The Jayhawks turned that play into another touchdown by Sims from two yards out to give KU a 24-7 lead over the Mountaineers just five minutes into the second half.
The Jayhawks would another touchdown late after another Millard interception.
WVU couldn't muster a scoring drive until the 4:54 mark of the fourth quarter mark and again later with 28 seconds to play in a very disappointing finish for the Mountaineers that will leave them home for bowl season.