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.
Colorado State graduate transfer John Gillon has chosen Syracuse, giving the Orange a potential starter at point guard entering the 2016-17 season.
DeSean Murray, who averaged 20.2 points as a sophomore at Presbyterian, will transfer to Auburn to play for coach Bruce Pearl.
Former Kentucky guard Ed Davender, the only Wildcat with at least 1,500 points and 400 assists, has died. He was 49.