Ash threw a 48-yard TD pass to Mike Davis and a 40-yard touchdown to Shipley, and Josh Turner took a blocked punt back 34 yards to help Texas blow the game open in the second quarter.
Steele Jantz was 28 of 51 passing for 251 yards and a late TD pass for Iowa State, which looked nothing like the team that stunned Texas 28-21 last season.
The mistake-prone Cyclones lost two fumbles, and Jantz added a pick in the first half. They didn't score until James White's 2-yard TD run with 11:33 left.
The Longhorns have now won two straight on the road against teams that beat them in Austin last year.
Texas thumped UCLA 49-20 in the Rose Bowl two weeks ago -- and it faced even less resistance from the Cyclones.
This was one of the biggest home games in recent memory for Iowa State, which had rallied from fourth-quarter deficits to win each of its first three games.
Part of the reason the Cyclones had to make such comebacks was because they kept turning the ball over early and often.
This time, it finally caught up to them.
The Longhorns recovered a White fumble on the Cyclones' second possession and settled for a field goal. Iowa State fumbled it right back to them on the kickoff, and Fozzy Whittaker's 16-yard TD run off a direct snap made it 10-0 Texas just under 10 minutes in.
The Longhorns converted a pick into a 35-yard field goal from Justin Tucker to go ahead 13-0 late in the first quarter. Cornerback Leonard Johnson committed a personal foul to keep a Texas's drive alive, and Ash followed by hitting Davis -- who was yards ahead of the nearest defender -- for a 48-yard TD to give the Longhorns a 20-0 lead with 10:18 before halftime.
Texas didn't need any more help to turn a rough night into a brutal one for the Cyclones.
Freshman Mykke Thompson broke through to block Kirby Van Der Kamp's punt. The deflection plopped into the arms of fellow freshman Turner, whose 34-yard touchdown return made it 27-0 with 4:30 left in the second quarter.
As if that wasn't enough for the brow-beaten Cyclones, Texas closed the half with a bit of trickery that worked to perfection.
Whittaker took the snap and handed it off to Shipley, who then flipped it to Ash on a reverse. Shipley then took off for the end zone, and Ash found him for a 40-yard TD pass and a 34-0 lead just over three minutes later.
Case McCoy got the start for the Longhorns and finished 7 of 12 passing for 110 yards, but he got much of his work after the outcome had been decided.
Iowa State had two apparent touchdowns called back because of penalties on a drive late in the third quarter.
Even White's TD run was marred by an injury to star tackle Kelechi Osemele, who had to be helped off the field.
Johnson was then taken off on a stretcher after helmet-to-helmet collisions with linebacker Jake Knott and defensive lineman Stephen Ruempolhamer while finishing off a tackle in the fourth quarter.
Johnson landed face down on the turf. He was flipped over, placed on a backboard and taken away by medical personnel. But Johnson waved to the crowd as he left, drawing cheers from the Iowa State crowd.
Jantz added an 18-yard TD pass to Chris Young with 3:50 left.
Though the Cyclones beat the Longhorns in Austin last year, this one fell back in line with the history of this series. Texas improved to 8-1 against Iowa State and 4-0 in Ames.
