The Longhorns (2-0) looked ready to be lassoed until taking a 13-10 lead just before halftime, although their defense had a great afternoon against a spread offense in preparation for next weekend's showdown with Texas Tech.
The defense held the Cowboys (1-1) out of the end zone and limited them to 3-for-17 on third down in helping to secure the Longhorns' 15th straight non-conference win, tying a school record established in the 1940s.
But their offense sputtered and their special teams were terrible. The Longhorns had a blocked punt that was returned for a touchdown and also a fake punt that didn't work and a fake field goal that failed.
McCoy completed 30 of 47 passes for 337 yards and three TDs with an interception. He missed 17 or more passes for just the third time in his career, including a dozen in the first half, when he was intercepted by linebacker Weston Johnson.
In what first-year Wyoming coach Dave Christensen called "probably the biggest game that's ever been played in the state of Wyoming," the Cowboys played a thrilling first half against the Longhorns, who were favored by 331/2 points.
Wyoming took a 10-6 lead with 92 seconds left before halftime when Luke Ruff blocked John Gold's punt and fellow freshman Ghaali Muhammad scooped up the bouncing ball and scampered 6 yards for the touchdown that gave the Cowboys their first lead.
This was the wake-up call for Texas, which scored the next 35 points, starting with a 25-yard TD toss from McCoy to James Kirkendoll that capped a six-play, 70-yard drive and gave the Longhorns a 13-10 halftime lead.
The Longhorns scored touchdowns on three of their four possessions in the third quarter to make it the rout most had anticipated.
They needed just five plays to score on McCoy's 9-yard keeper after D.J. Monroe returned the second-half kickoff 41 yards to the Wyoming 40. McCoy also threw a 33-yard scoring toss to Dan Buckner and Tre' Newton added a 13-yard TD run.
McCoy's 26-yard touchdown pass to John Chiles made it 41-10 midway through the fourth quarter and ended his day.
Before Kirkendoll's TD in the final minute of the first half, the 'Horns managed just two field goals on eight possessions, and Justin Tucker failed to gain the first down on a fake punt from the Texas 9, which led to Austin McCoy's 22-yard field goal that tied it at 3 early in the second quarter.
If that was their first alarm, the Longhorns hit the snooze button.
After Malcolm Williams' 34-yard kickoff return, McCoy hooked up with Kirkendoll for 43 yards and then scampered for an 18-yard gain, but once again the 'Horns stalled and settled for Hunter Lawrence's 32-yard field goal for a 6-3 lead.
The Longhorns, playing the Cowboys for the first time in 31 years and in Laramie for the first time ever, looked nothing like heavy favorites in the first half.
Maybe it was the altitude -- 7,200 feet, highest in all of college football -- or maybe they missed their band, which was absent at a Longhorns game for the first time since the 1984 Freedom Bowl. Athletic Director DeLoss Dodds explained it was both an economic decision and a matter of space.
The UT fans got 3,800 tickets to War Memorial Stadium, which seats 30,514, a far cry from the Longhorns' stadium where they opened the season last week in front of 101,096 fans, the largest crowd ever to watch a football game in the state of Texas.
A full band takes up 600 seats and a pep band a third of that.
The Longhorns completed just 3-of-11 third downs in the first half, but the Cowboys were worse: 1-for-9, and that kept Texas from paying dearly for its sputtering offense until they could get things figured out.