Tron Smith led the No. 21-rated Gaels with 15 points, and Diamon Simpson added 12 points and seven rebounds. The California school won its fourth straight game to improve to 21-3 overall and 8-1 in the WCC.
John Bryant led all scorers with 21 points and 12 rebounds for the Broncos, who have lost two of their last three to slip to 12-11 overall and 4-4 in the conference.
St. Mary's appeared to be in control of the game at 36-23 but Santa Clara went on an 11-1 tear capped by Ben Dowdell's layup with under 14 minutes to play and the game stayed tight the rest of the way.
Brody Angley, who finished with11 points and seven boards, had the Broncos' last chance to tie the game but his jumper rimmed out and Yusef Smith got the rebound and hit the final free throws to ice the game.
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