Thames grabbed seven rebounds and Shepard hauled down six as the Aztecs (19-1, 8-0 MWC) ran their winning streak to 18 games.
J.J. O'Brien supplied 10 rebounds to help hand Coach Steve Fisher his 300th career win with SDSU.
The Rams (12-10, 3-6) were led by Jon Octeus with 24 points.
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