Oregon quarterback Marcus Mariota scored on a 2-yard run midway through the third quarter and the Ducks sent kicker Alejandro Maldonado out to kick the extra point.
Kansas State's Javonta Boyd blocked the kick and the ball ended up in the hands of teammate Chris Harper, who was tackled in the end zone.
After a review of the play, the officials awarded the Ducks a 1-point safety that put them up 32-10.
It was the first such 1-point safety in major college football since Texas got one against Texas A&M in 2004, STATS said.
Oregon defeated Kansas State 35-17 in what may have been coach Chip Kelly's final game with the Ducks.