Memphis(2-0) won 87-76, and advanced to play in New York's Madison Square Garden next week while Alabama (1-1) will return to play on Sunday against Alabama State.
Alabama trimmed what was an 18-point Memphis second-half lead to a nine-point deficit on three Justin Jonus free throws with 4:23 to play.
"That was one stretch in the game we thought we defended them pretty well," Alabama Coach Mark Gottfried said. "We've played three games and we haven't defended very well. We've got to make a decision on whether we want to be a good defensive team. We haven't done that yet."
Alabama faltered on subsequent possessions, however, suffering a backcourt violation and a turnover on a miscommunication between Ronald Steele and Evan Brock on its next two trips down the floor.
Memphis put clamps on Jonus after the three free throws late in the game, not allowing him to get off another uncontested shot. Jonus had just one point over the last four minutes of the game.
"We were our own worst enemy," Gottfried said. "We hurt ourselves when we needed to be helping ourselves. We've got a couple of you guys who are playing at key times and they have to come on for us."
Memphis extended its lead to 11 points afterwards and fouls were traded through the end of the game. Memphis guard Darius Washington led all scores with 23 points and six assists.
For Bama, Jonus had a team and personal career high with 18 points, hitting 4-of-6 three point attempts. Jonus added 6-of-7 shooting from the free throw line. Junior Jermareo Davidson had a career night with 19 points and 13 rebounds along with four blocked shots. Chuck Davis was the third and final Alabama player in double figures with 15 points and five rebounds. Davis was limited with foul trouble and picked up his fifth foul with three and a half minutes to play.
"When you play a game this early with a guy like Chuck not playing a lot of minutes it hurts your team," Gottfried said. "There weren't a lot of areas in thee game where you can say Alabama was pretty good."
Gottfried was disappointed with the defensive effort.
"I think with our basketball team we have a lot of work to do," he said. "We had a lot of break downs defensively; on offense we have to learn what a good shot is. Our shot selection was not very good. This basketball team needs to learn how to become a good basketball team."