Levi Randolph contributed nine rebounds as the Crimson Tide (17-8, 9-3 Southeastern Conference) won its third straight game, while the Gamecocks (12-13, 2-10) lost their sixth straight.
Trevor Releford had two steals, giving him 170 for his career and moving him ahead of Robert Horry for third on the school's all-time steals list. The junior needs seven steals to tie Senario Hillman, Alabama's career leader.
The Tide, which had not scored more than 60 points in its last eight games, opened the game by bolting to a 32-9 lead, topped off by a field goal by Cooper at the 5:55 mark. The run was triggered by six 3-point baskets, two each by Lacey and Retin Obasohan and one each from Releford and Cooper.
South Carolina started out by missing its first eight 3-point attempts. The Gamecocks then outscored the Crimson Tide 15-5 to trim the lead to 35-24 when Ellington banked a 3-pointer just prior to the halftime buzzer.
In the second half South Carolina sliced the lead to 39-29, the closest that the Gamecocks would get, but the Crimson Tide responded with a 14-4 run to extend the lead to 53-33 on two free throws by Releford with 11:04 to go.
Maryland point guard Melo Trimble, considered a lock to leave the program before struggling in the second half last season, has withdrawn from the NBA draft and will return for his junior season.
Louisville's Chinanu Onuaku, who recently underwent a medical procedure to correct a heart rhythm issue detected during the combine, will keep his name in the NBA draft pool.
Andrew White III will return to the Nebraska men's basketball team next season after removing his name from the NBA draft.