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.
Nike Men's Tennessee Volunteers Tennessee Orange ELITE Shooter Long Sleeve ShirtShop
Thurl Bailey, a member of the 1983 NC State title team, has helped get the Wolfpack an invitation to the White House to meet President Barack Obama on May 9.
It's about time for someone other than Duke and Kentucky to grab the top class. Could it be Shaka Smart and Texas in 2017?
Which teams have enjoyed the most NCAA tournament success since 2000? Kansas' recent run to the Elite Eight vaulted the Jayhawks up the list.