McBride, whose previous best was 13 points, hit 12 of 15 shots and 7 of 9 free throws. He also had career-high eight rebounds.
The Knights (4-1) shot 52 percent (24 of 46) from the field and held the Wildcats (2-5) at bay by making 13 of 19 free throws in the second half to finish 19 of 25 for the game.
UCF led 39-30 at halftime but with 10:21 left Ricky Johnson's jumper made it a two-point game. McBride got his eighth rebound on a tip-in with 1:29 left and got behind the defense for a dunk that turned into a three-point play at 56 seconds for a 74-65 lead.