Stoops posted his 145th victory with Oklahoma. He is 12 wins shy of tying Barry Switzer for the most in school history.
Brennan Clay ran for a career-best 157 yards as the Sooners bounced back from a loss to Notre Dame. Oklahoma (6-2, 4-1 Big 12) has won 20 straight following a defeat in the regular season.
Jones' 20-yard TD pass to Justin Brown to open the second half put the Sooners up 21-6. Oklahoma racked up 593 yards of offense, and put it away when Jones' 31-yard TD pass to Kenny Stills made it 35-13 with 10:59 left.
Steele Jantz threw for 191 yards for Iowa State (5-4, 2-4). The Cyclones lost their 21st straight home game against the Sooners, a stretch of futility that dates back 52 years.
Oklahoma outgained Iowa State 325-84 in the first half, just a week after scoring a season-low 13 points in its 30-13 loss to Notre Dame. But it took a 21-yard TD pass from Jones to Stills with 14 seconds in the first half to go ahead just 14-6.
The dominant Sooners caught a break in the third quarter.
Iowa State's Jeremy Reeves got a hand on Jones' try into the end zone. But Reeves' deflection only made it easier for Brown to grab Jones' third touchdown pass of the day.
The Cyclones answered quickly, as Jarvis West scored on a 19-yard end-around run to pull them within 21-13. Oklahoma systematically wore down Iowa State's defense, running 68 plays through three quarters, and Clay's 18-yard TD run made it 28-13 Sooners with 2:04 left in the third quarter.
It was the 10th time Jones has thrown for 400 yards in his illustrious career, and the Sooners converted on nine of 14 third downs.
Oklahoma was held scoreless in the first quarter for the first time this season. But Iowa State couldn't keep Jones and the Sooners off the board forever, as Jones threw a 20-yard TD pass to Sterling Shepard with 10 minutes left in the first half to give Oklahoma a 7-0 lead.
Jones completed 16 of his first 22 passes. But his 23rd and 24th tries landed in the waiting arms of Iowa State safety Durrell Givens.
The Cyclones turned their good fortune into field goals of 27 and 51 yards by Edwin Arceo late in the second quarter. Settling for three points instead of seven, however, came back to haunt Iowa State.
A pair of strong runs by Clay convinced Oklahoma to take a crack at the end zone with under a minute left before the break. Jones hit Brown for 40 yards and Stills for a 21-yard TD, and the Sooners went ahead 14-6 at halftime.
Iowa State played its first game without star linebacker Jake Knott. He was the Big 12 defensive player of the week in a win over Baylor despite a shoulder injury that will cost him the rest of the season.
Damien Williams, Oklahoma's leading rusher with 581 yards entering play, didn't start after injuring his ankle last week.
Williams has just 7 yards on three carries. But Oklahoma still had no trouble thumping an opponent it has owned for generations.
The Sooners are now 70-5-2 against Iowa State and a perfect 8-0 under Stoops.
The last time the Cyclones beat Oklahoma in Ames was in 1960 — three days before John F. Kennedy was elected president.
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