Shrigley came off the bench to hit five field goals, including 4-of-7 tries from the 3-point range, in the Aztecs' (23-2, 12-1 MWC) second consecutive victory.
Davis also had eight rebounds and Skylar Spencer chipped in with 10 points.
Xavier Thames, San Diego State's leading scorer this season, was a pedestrian 1-of-9 from the field and ended with four points. He contributed with five rebounds and five assists.
Utah State (15-11, 5-9) was led by Jarred Shaw and Spencer Butterfield, who both scored 10 points. The Aggies shot 34 percent from the field and have lost back-to-back games after winning three in a row.
San Diego State led 35-22 at halftime, which was enough of a buffer to hold off Utah State in an evenly played second period.