For the 28th consecutive year since the NCAA Tournament was expanded to 64 teams, the four No. 1 teams won their opening game of the event.
Kansas, however, came close to being the first of those top seeds to fall. The Jayhawks found themselves in a ferocious duel with the Hilltoppers and only at the very end of the contest were they able to open a lead.
The 7-foot Withey scored 17 points, grabbed six rebounds and blocked seven shots. He made 7-of-9 from the field and protected the inside when the Jayhawks needed someone to come through.
Kansas will face North Carolina in the next round on Sunday with Tar Heels coach Roy Williams going up against his former team. North Carolina held off Villanova earlier in the evening 78-71.
Naadir Tharpe and Ben McLemore combined to make six consecutive free throws for Kansas in the final minute to keep it a two-possession game and prevent Western Kentucky from having a chance to pull off a last-second stunner.
McLemore and Travis Releford both had 11 points for the Jayhawks (30-5).
Western Kentucky, which won the Conference USA Tournament as the No. 6 seed, was led by Jamal Crook with 13 points and nine rebounds.