Johnson spun in the paint and hit his patented hook shot with 1:03 remaining to give WKU a 76-73 lead and after Nick Rakocevic answered with a layup, Johnson went 1 of 2 at the free-throw line at 33.1.
USC freshman Jordan Usher air-balled a 3-pointer with 24.2 left and the Trojans didn't foul, allowing Dwight Coleby to seal it with a dunk at 11.3.
Coleby finished with 13 points, Lamonte Bearden had 11 and Josh Anderson 10 for WKU (26-10), which plays Oklahoma State in the quarterfinals on Wednesday night.
WKU extended its made 3-pointer streak to 974 consecutive games, dating to March 15, 1987, for fifth-longest in the nation behind UNLV, Vanderbilt, Duke and Arkansas.
Elijah Stewart led USC (24-12) with four 3-pointers and 20 points.
