The Aztecs thus set up an unlikely third-round tournament meeting with Florida Gulf Coast, which in its initial appearance in the event stunned Georgetown earlier in the evening 78-68.
Playing as the No. 7 seed in the South Region, San Diego State battled the Sooners to a standoff through the game's first 30 minutes.
The Aztecs then pulled off its sudden outburst and Oklahoma could never recover. San Diego State was two of the five teams from the Mountain West Conference participating in this year's tournament to win a game.
Colorado State managed a victory, but Boise State, New Mexico and UNLV all lost in their first game.
Jamaal Franklin scored 21 points to lead the Aztecs (23-11), who fell to New Mexico in the semifinals of the MWC Tournament. James Rahon came off the bench to add 17 points while Tapley had 10.
San Diego State went 16-of-17 from the foul line while Oklahoma went to the stripe only eight times, making four.
Romero Osby was close to a one-man show for the Sooners (20-12), scoring 22 points to go with eight rebounds. No other Oklahoma player had more than eight points.