Card, who has started three straight games but may be replaced next week if freshman Quinn Ewers returns from a clavicle injury, finished with 303 yards passing.
His 15-yard scoring pass to Worthy just before he took a hard shot to his midsection opened the scoring. Those two connected again early in third quarter when a leaping West Virginia defender let a deep pass slip through his hands and tipped it to Worthy as the Longhorns receiver was falling down.
Worthy also threw a touchdown pass to Ja'Tavion Sanders on a trick play in the second quarter.
Worthy finished with 119 yards receiving. Texas (3-2, 1-1) avoided its first 0-2 start in the Big 12 since 2016 heading into next week's rivalry game with Oklahoma.
JT Daniels passed for 253 yards for West Virginia (2-3, 0-2). The Mountaineers got a scare in the third quarter when freshman running back CJ Donaldson was carted off on a stretcher after taking a blow to the head. His helmet and shoulder pads were removed, but he appeared to give a “thumbs up” signal with his right hand as he was taken off the field.
West Virginia: The Mountaineers' early plan abandoned the pounding run game that had helped win the previous two games. West Virginia came in averaging 217 yards on the ground but eight of the first nine plays were pass attempts. By the time the Mountaineers were down 28-0, it was too late to return to a grind-it-out attack. West Virginia finished with 61 yards rushing.
Texas: A defense that couldn't get off the field in the second half and gave up six fourth-down conversions in a loss a week earlier to Texas Tech was dominant and aggressive up front against the Mountaineers. Texas snuffed West Virginia's fourth down attempt on the second series and forced four punts in the first half. The Longhorns sacked Daniels three times.
West Virginia hosts Baylor on Oct. 13.
Texas plays No. 18 Oklahoma in Dallas next Saturday.
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