Santa Clara was 13 of 14 from the foul line, but the one miss came with five seconds left when Clark could have given the Broncos a four-point lead.
Pepperdine's Jeremy Major narrowly missed a 3-point attempt at the buzzer.
Nate Kratch added 10 points for SCU (11-10, 5-4 West Coast), which moved into a third-place conference tie with Pepperdine (12-8, 5-4) and BYU.
Brownridge had 11 points in the first half as Santa Clara led 29-15 on its way to a 35-24 advantage at the intermission. The Broncos missed 11 of their last 12 field goals in the second half.
The Waves used a 10-2 run to get within 53-51 with 5:08 left. Stacy Davis led Pepperdine with 21 points and nine rebounds.