Southern Mississippi, Texas-El Paso and Tulsa also won their way into the semis, but Memphis will be the favorite the rest of the week to win a record seventh league tourney title.
Memphis will leave next season for what is now the Big East Conference.
Crawford scored 24 points in boosting the Tigers to 28-4. Memphis shot 55 percent for the game with Adonis Thomas contributing 17 points.
Memphis will face Tulsa in the semifinals after the Golden Hurricane got past East Carolina 79-72.
Scottie Harrelson led Tulsa with 22 points and James Woodard contributed 17. Tulsa will take a 17-14 record into its meeting with Memphis.
Southern Mississippi, seeded second in the tourney, had no trouble putting away Alabama-Birmingham 81-66 in their quarterfinal contest.
Neil Watson scored 23 points off the bench and Dwayne Davis had 20 for the Golden Eagles (24-8). Southern Mississippi built a 14-point halftime lead.
The Golden Eagles will now face Texas-El Paso, which disposed of Houston 80-69.
Julian Washburn scored 20 points for the Miners (18-13), who handed Houston its first loss in five games.