Gilgeous-Alexander went 10 for 12 and made both of his 3-point attempts to send fifth-seeded Kentucky (26-10) to the Sweet 16 for the second straight season.
It wasn't a runaway until the last 7 minutes.
Buffalo (27-9), which got here with a 21-point blowout over Arizona, twice trimmed a double-digit lead to five midway through the second half. Gilgeous-Alexander answered both times — once with a 3-pointer to extend the lead to eight, then again a few minutes later with a three-point play that started a 12-2 run and put the game away.
Wes Clark had an electric day for the Bulls again, but it wasn't enough. He finished with 26 points but closed his career at 0-5 against the Wildcats.