San Diego State will face the surprising Baylor Bears in one of the semifinals at Madison Square Garden next Tuesday. The other semifinal will send Penn State against Notre Dame. The championship game will be played April 2.
The Aztecs owned an 11-point halftime lead between the two California schools, but Saint Mary's rallied to tie it with 2 minutes to go.
Shelton's jumper gave San Diego State a 66-64 lead and the Aztecs stayed in front the rest of the way.
Richie Williams made 1-of-2 foul shots with 14 seconds left, giving San Diego State a 69-66 advantage. Saint Mary's hopes of forcing overtime were dashed when Patrick Mills turned the ball over with 11 seconds remaining.
Williams then added another free throw for the final margin.
Billy White led the Aztecs (26-9) with 17 points, hitting 8-of-12 from the field. Saint Mary's (28-7) was led by Mills with 18.
San Diego State was the only one of the four No. 1 seeded teams to reach the semifinals. Auburn, Creighton and Florida had been the No. 1 seeds in their quarters of the bracket.