Isaiah Austin added 13 points and seven rebounds for the Bears (25-11), who missed the tournament last season after reaching the Elite Eight in 2012. Brady Heslip and Rico Gathers tallied 12 and 11 points, respectively.
Baylor, which went 38-for-48 from the foul line, will play either 14th-seeded Louisiana or third-seeded Creighton in the third round on Sunday.
Terran Petteway ended with 18 points but went 0-for-7 from beyond the arc for the Cornhuskers (19-13), who fell to 0-7 in NCAA Tournament action. Shavon Shields and Ray Gallegos had 16 and 15 points, respectively.
Nebraska coach Tim Miles was ejected after getting whistled for two technical fouls in the second half.