JaMychal Green, a first-team All-Southeastern Conference forward, finished with nine points and five rebounds in 22 minutes for the Crimson Tide (11-3). Green did not start, but played for the first time since injuring his right shoulder in a Dec. 17 loss to Kansas State.
Alabama, which has won three straight and four of five, opens its SEC schedule Saturday at Georgia.
Kammeon Holsey finished with 14 points for Georgia Tech (7-7), which has lost three straight. The Yellow Jackets dropped to 0-2 at Philips Arena, where they will host No. 5 Duke in both schools' Atlantic Coast Conference opener Saturday.
After Green's finger-roll gave the Crimson Tide a 40-22 lead to end the first-half scoring, Georgia Tech's Julian Royal made it 41-31 on a layup with 17:11 remaining.
But less than 5 minutes later, the Crimson Tide led by 22 following two free throws by Andrew Steele.
Tuesday marked Steele's first game since suffering a concussion in last year's SEC tournament. The junior guard finished with nine points, including a three-point play that made it 60-37 with 10:13 remaining.
Yellow Jackets coach Brian Gregory did not start Glen Rice Jr., who went scoreless in a 72-66 loss at Fordham last week and was suspended three games to begin the season after breaking a team rule. Rice finished with five points and went 2 of 7 from the field.
Royal added 10 points for Georgia Tech, which ranks No. 235 in assists-to-turnover ratio and committed 22 turnovers with 12 assists.
Mitchell moved right to left along the baseline and took a pass from Releford for a dunk that gave the Crimson Tide a 26-15 lead with 8:39 left in the first half.
Releford followed with a fastbreak layup 4 minutes later to put Alabama up 34-20.