Chelf completed 19-of-25 passes and also caught a scoring pass as the Cowboys (10-1, 7-1 Big 12) reeled off a seventh straight win.
Kye Staley rushed for a pair of scores and Tracy Moore made five catches for 126 yards with a touchdown as OSU helped its drive for a Big 12 championship.
The Cowboys need to either beat No. 18 Oklahoma Dec. 7 or see Baylor lose to either Texas Christian or Texas to win the Big 12's automatic Bowl Championship Series berth.
The Bears (9-1, 6-1), meanwhile, fell out of the running for a national title as their 13-game winning streak was ended.
Bryce Petty made good on 28-of-48 passes for 359 yards and two touchdowns for Baylor.
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