Releford scored all of his points in the second half and made two free throws with 8 seconds left for the Crimson Tide (9-6, 1-1 Southeastern Conference), which had lost three of four games. Then Trae Golden missed a potential tying 3-pointer at the buzzer to send the Volunteers (8-6, 0-2) to their third straight loss.
Levi Randolph scored 12 for the Tide. Andrew Steele had 11 points and four steals and helped spark a 10-0 late run for Alabama, which used a full-court press to force three turnovers during that spurt. The Tide was 15-of-24 shooting in the second half (63 percent) after struggling to a 27-percent clip (8 of 30) before halftime.
Jordan McRae scored 21 points for Tennessee in his third straight game with 20-plus points.
Steele scored six straight points then made a steal and dished to Releford for a layup and a 62-55 lead with 2:55 remaining. It was the Tide's biggest lead of the game after trailing by eight in the first half.
Golden answered with two drives and a free throw to make it 62-60 with 1:52 remaining but then missed a shot going for three in a row. Lacey responded with a jump shot and fast-break layup.
Lacey then missed a contested 3-pointer after Alabama ran most of the shot clock down. McRae cut it to 66-65 after following his own missed shot with 8 seconds left.
Releford was quickly fouled and made both attempts, leaving the Vols with one last chance that didn't go down.
Tennessee had a nice turnaround defensively after giving up 85 points to Memphis and 92 to Mississippi in back-to-back defeats, holding to Alabama to 24 points in the first half.
Releford, who had a career-high 26 points Wednesday night in a loss at No. 10 Missouri, missed all three field goal attempts in the first half and then had eight points in the first 3:06 to open the second.
He helped lead Alabama to an 18-9 run out of the locker room for a five-point lead that was Alabama's biggest until the final minutes
Tennessee took a 28-24 lead into halftime after McRae made 2 of 3 free throws with one second left. Lacey had missed a free throw on the other end and then fouled McRae on a 3-point shot.
Alabama was just 4-of-21 shooting from inside the 3-point line before the half, including a couple of droughts with at least seven consecutive misses.
Tennessee outrebounded Alabama 40-25 but also committed 16 turnovers to the Tide's seven.
Golden and Josh Richardson both scored eight points for the Vols.
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Mike Krzyzewski says he has good reason to be excited for next season thanks to a combination of Duke's incoming freshmen and a core of experienced upperclassmen.
Georgia guard Juwan Parker has been awarded a medical redshirt, leaving him with two years of eligibility, after missing the 2015-16 season with a partially torn Achilles tendon.
Forward Trevon Bluiett has withdrawn from consideration from the NBA draft and will return to Xavier for his junior season.