Tapley finished with 19 points overall while Jamaal Franklin struck for a game-high 23 as the Aztecs (14-2, 2-0 MWC) won for the third straight time.
Xavier Thames also helped out with 14 points in San Diego State's triumph.
The Rams (13-3, 0-1) were led by Wes Eikmeier with 22 points as their seven-game winning streak was broken.
Colton Iverson supplied a double-double of 18 points and 11 boards in the loss.
Celebrity Breakups and divorces of 2014 [PHOTOS]