Santa Clara scored the game's first two points and Gonzaga then produced the next 15 on the way to a 44-15 halftime lead.
The Bulldogs shot 56 percent from the field with Harris scoring 15 points and Kelly Olynyk adding 14.
Gonzaga (26-2, 13-0 West Coast Conference) has a two-game lead over St. Mary's in the league race with three games to play.
Brandon Clark scored 14 points and was the only player in double figures for the Broncos (19-9, 7-6).
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