In a meeting of teams that had their national championship hopes derailed by late-season losses, Oregon won for the fourth time in its last six bowl appearances.
Mariota threw for 166 yards and Kenjon Barner ran for 143 more. The Ducks, who finished the regular season ranked fourth in the BCS standings, could move as high as second thanks to a loss in the Sugar Bowl by No. 3 Florida.
The game was played amid speculation that Oregon Coach Chip Kelly could fill one of the current coaching vacancies in the NFL. He is expected to interview with multiple teams during the next week.
De'Anthony Thomas ran the opening kickoff back 94 yards for an Oregon touchdown and he then caught a 23-yard pass from Mariota to give the Ducks a 15-0 lead after one quarter.
Kansas State soon climbed within 15-10 and the Wildcats appeared ready to take the lead when they marched inside the Oregon 20-yard line. Kansas State lined up as if to go for it on 4th-and-1 from the Oregon 18, but the Wildcats were called for a motion penalty and then missed a field goal that would have brought them within two.
Oregon dominated from that point, getting a 24-yard scoring pass from Mariota to Barner with 14 seconds left in the half to seize a 22-10 lead at the break.
Mariota added a 2-yard touchdown run in the third period and Alejandro Maldonado tacked on two field goals for Oregon, which finished the year at 12-1. Its only loss was a three-point setback against Stanford on Nov. 17.
Kansas State wound up at 11-2, having had its bid for an unbeaten season halted by Baylor the same day Oregon lost to Stanford.
The Wildcats have appeared in a bowl game five times over the last 10 years and they have lost them all.
Kansas State quarterback Collin Klein, a finalist for this season's Heisman Trophy, went 17-of-32 for 151 yards with one touchdown and two interceptions.