The Crimson Tide (16-8, 8-3 Southeastern Conference) won for the eighth time in 10 games with another stifling defensive effort. Alabama has held nine consecutive SEC opponents to less than 60 points, limiting the Bulldogs to 31 percent (16 of 52) from the field.
Georgia (12-12, 6-5) went more than 10 minutes without a field goal in the second half but still had a chance because of both teams’ offensive woes.
When Donte’ Williams slammed in a wild miss off the backboard, the Bulldogs led 41-40 with 2:37 remaining.
But Randolph swished a 3-pointer, and Cooper followed with another to finish off Georgia.
Cooper led the Crimson Tide with 14 points – no one else on the winning team was in double figures.
Alabama prevailed despite shooting just 39 percent (19 of 49) and getting beat on the boards, 41-33.
Kentavious Caldwell-Pope scored 22 points for the Bulldogs, and Nemanja Djurisic added 12. But Georgia didn’t have another player with more than four points, a staggering display of offensive ineptitude that might have ended any hope of making an improbable late-season run for NCAA Tournament consideration.
The teams meet again March 9 in Tuscaloosa, the regular-season finale for both.
Georgia was trying for its first six-game winning streak in the SEC since 2001, coming into the game tied with Kentucky for the longest active run in the conference.
Both teams lost Tuesday, with the Wildcats falling at Florida.
The Bulldogs jumped out to a quick 7-0 lead and pushed the margin to 15-6 on a jumper by Caldwell-Pope. But Alabama dominated the rest of the half, as Georgia went nearly 4 minutes without scoring in a preview of what was to come over the final 20 minutes. The home team missed five straight shots along with a turnover, allowing the Tide to close the half on a 19-7 run.
Alabama went to the locker room with a 25-22 lead after Trevor Lacey’s layup with 27 seconds remaining.