The Mountaineers' Kevin White finished with six catches for 132 yards and matched Stedman Bailey's school record of five straight games with 100 receiving yards.
West Virginia jumped ahead 26-0 at halftime and cruised from there.
Kansas (2-3, 0-2) managed little offense in the debut for interim head coach Clint Bowen, who took over after Charlie Weis was fired on Sunday. The Jayhawks were held to 176 totals yards and nine first downs.
Kansas lost its 26th straight road game. The busiest player for the Jayhawks was Trevor Pardula, who punted 14 times.
Kansas quarterback Montell Cozart, who had four interceptions in a 23-0 loss to Texas last week, couldn't move the offense again and played only the first half. Two other quarterbacks had no better luck in the second half.
West Virginia amassed 557 yards of offense but its special teams had an up and down day.
After the Mountaineers' Jordan Thompson fumbled a punt on his 18 that led to a short touchdown run by the Jayhawks' Corey Avery, Alford took the ensuing kickoff down the right sideline for a score to put West Virginia ahead 33-7 late in the third quarter.
Late in the game, the Jayhawks' Nick Harwell returned a punt 76 yards for a TD, the third straight game that West Virginia's special teams allowed a score.
The margin of victory could have been much greater. West Virginia had another field goal attempt blocked and Dustin Garrison fumbled the ball away at the Kansas 5 following a 28-yard run.
Trickett completed 20 of 35 passes with an interception. Several of his incompletions were long throws. White and Alford both let passes go off their hands in the end zone, resulting in two of Lambert's three first-quarter field goals.
White got loose in single coverage late in the quarter and Trickett found him in stride for a 63-yard TD for a 16-0 lead.
Alford turned a screen pass into a 39-yard gain late in the second quarter, leading to Shell's short TD run. Lambert, who earlier had field goals of 42, 25 and 43 yards, capped the first-half scoring with a 53-yarder as time expired.