It was the 18th straight conference opening win for the Jayhawks, who've won the last four Big 12 titles.
Kansas (12-4, 1-0) jumped on Kansas State at the start, scoring the game's first 18 points. But the young Jayhawks got sloppy, letting Kansas State get within three before pulling away in the second half.
Cole Aldrich had 15 points for Kansas, which has won 34 straight games at Allen Fieldhouse and 37 of 39 meetings against Kansas State.
The Wildcats (11-5, 0-2) clawed their way back from the big early hole with pesky defense, but they couldn't keep Collins and Taylor out of the lane and had no answer for Aldrich inside.
Jacob Pullen led Kansas State with 13 points.