Kansas (27-5) went 3-0 versus the Red Raiders this season, outscoring Texas Tech (11-20) by an average of 26.3 points.
The Jayhawks draw Iowa State, a team that has given them trouble this season, in Friday's semifinals. Iowa State beat Oklahoma 73-66 in its Big 12 quarterfinal.
Kansas jumped out to a 15-2 lead Thursday with McLemore getting 12 points. Texas Tech pulled closer but never seriously threatened.
The Jayhawks led 34-25 at halftime and drew away throughout the second half, leading by 20 with 14:59 to go when Travis Releford made a free throw and 25 less than 6 minutes later. Kansas was up by as many as 34 as time wound down.
McLemore connected on eight of his 12 shots in getting to 24 points. Deep reserve Rio Adams, playing late, had 11 points but no other Kansas player reached double figures although nine other had points.
Dejan Kravic paced Texas Tech with 20 points.