The Aztecs held the Gauchos scoreless during a 5-minute stretch early in the game while turning a one-point deficit into an 18-5 lead.
Tapley led the way with 23 points, Jamaal Franklin added 14 and J.J. O'Brien had 12. San Diego State went 11-of-17 from 3-point range and led by as many as 26 points in the second half.
The Aztecs have won seven in a row since losing their season-opener to Syracuse.
California-Santa Barbara (3-5) was led by Kyle Boswell's 23 points.