Levi Randolph hit a pair of 3-pointers and led the top-seeded Crimson Tide (23-12) with 16 points.
Retin Obasohan added 14 points to the Alabama totals and Trevor Releford and Nick Jacobs both scored 10 points.
Fourth-seeded Stanford (19-15) was led by Chason Randle, who scored 11 points. Robbie Lemons scored 10 points and was the only other Cardinal player in double figures.
Alabama led 32-24 at halftime but Stanford whittled the lead down to 54-50 on Aaron Bright's 3-pointer with 5:41 to play in the game. The Tide responded with seven unanswered points to regain control.
Celebrity Families of 2014 [PHOTOS]