Kenjon Barner ran for 143 yards on 31 carries and scored on a 24-yard touchdown pass from Marcus Mariota in the second quarter. Mariota later scored on a 2-yard run in the third quarter, capped by an obscure 1-point safety that went in the Ducks' favor.
Even Oregon's defense got into the act, intercepting Klein twice and holding him to 30 yards on 13 carries.
"We got beat by a better team tonight, combined by the fact that we let down from time to time," coach Bill Snyder said after Kansas State's fifth straight bowl loss.
Whether Kelly leaves Eugene or not, he had a good run, leading the Ducks to four straight trips to BCS bowls, the last two wins.
Ducks fans sure let him know how they felt, chanting "We want Chip!" just before he was handed the massive Fiesta Bowl trophy.
"Our focus was on this game tonight," Kelly said. "If for some reason, someone wanted to talk to me, it's because of those players over there. We have an unbelievable team, an unbelievable program and any success is because of those guys."
The 2013 version was an upgrade: Nos. 4 and 5 in the BCS, two of the nation's best offenses, dynamic players and superbly successful coaches on both sides.