The Jayhawks won their 31st straight home game, but had to work hard to get the victory in what was the opening game of the Big 12 Conference season for both teams.
McLemore made all six of his 3-point tries, one of them coming in the final second of regulation to bring about the extra period.
Kansas then raced to a 90-79 lead in overtime while lifting its record to 13-1. It was the Jayhawks' 12th straight victory.
McLemore scored 33 points and Jeff Withey added 15 points and 12 rebounds for Kansas.
The Jayhawks outshot Iowa State 50 percent to 41, but the Cyclones made six more 3-pointers than did Kansas.
Melvin Ejim had 19 points, 11 rebounds and five assists for Iowa State (10-4), which had a four-game winning streak halted.
Kansas has won 13 of its last 14 meetings with the Cyclones.