Ash's touchdown run came on Texas' sixth play from scrimmage. Mike Davis caught a 22-yard touchdown pass just before halftime. In the third quarter, Ash flipped the ball to Daje Johnson in the backfield and the freshman scooted around the end for a 45-yard TD.
Ash was 16 of 22 for a career-high 221 yards for Texas (2-0).
New Mexico (1-1) held the ball for nearly 20 minutes in the first half, but starting quarterback B.R. Holbrook was knocked out of the game in the second quarter after taking a blow to the helmet on a tackle.
Texas coach Mack Brown had said he wanted to see Ash get more comfortable in the passing game, especially throwing deep. What the Longhorns got was another solid performance by a quarterback still feeling his way through the offense.
Ash misfired on his deep throws early and was sacked twice in the first half, but again showed he can manage a short passing game and use his legs to make big plays.
The touchdown run came when Ash rolled right, cut up field and spun back to his left, scampering past three defenders in the middle of the field to break into the open.
New Mexico, which won just one game each of the previous three seasons, controlled the ball for large chunks of the first half, using its triple-option offense to grind out first downs and minutes.
But the Texas defense refused to yield any points and delivered a crushing hit midway through the second half that took away any chance the Lobos had of keeping it close.
Holbrook, who had done a good job keeping Texas off balance throwing and running, picked up a first down was sliding to go down when Texas cornerback Quandre Diggs clocked him with a helmet-to-helmet hit. New Mexico's first-year coach Bob Davie screamed for a penalty and didn't get one.
Holbrook was helped off the field and escorted to the locker room, leaving the New Mexico offense in the hands of freshman Cole Gautsche. Gautsche threw an interception to Diggs on his pass attempt. Holbrook was 5 of 8 for 32 yards and had 39 yards rushing when he left.
Texas had just four offensive possessions in the first half and scored three times. Ash let his receivers do the work on the touchdown throws.
Davis' touchdown came in the final minute of the half. He was running to his left when he caught a short pass just across the line of scrimmage and quickly turned past a defender to find a lane to the end zone to make it 17-0.
The Longhorns scored at the start of the third quarter when Johnson took a shovel pass and zipped around the right end for another touchdown. Joe Bergeron and D.J. Monroe added late touchdown runs for the Longhorns.
Ash came out of the game at the start of the fourth quarter for Case McCoy, who threw a 13-yard touchdown pass to M.J. McFarland, for the final score.
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