Moody hit 13 of 14 free throws and White made 4 of 5 shots from distance.
Aaron Jones added 10 points as Mississippi (20-10, 11-6 Southeastern Conference) recorded its seventh 20-win in nine years.
Mississippi trailed 43-38 early in the second half before going on a 17-3 run for a 55-46 advantage. Six Ole Miss players scored during the stretch, including back-to-back 3-pointers by White.
Alabama pulled within 75-70 with under a minute left, but Mississippi made 7 of 8 free throws to seal it.
Levi Randolph led Alabama (17-13, 7-10) with 32 points after going perfect from the line on a school-record 17 attempts.
Rodney Cooper added 14 for the Crimson Tide and Jimmie Taylor had 13 points with 11 rebounds.
The Rebels spoiled Senior Night for Randolph and Cooper in their final games at Coleman Coliseum.
Mississippi took its first lead of the game 34-32 on a 3-point shot by White with 17:57 remaining. The teams played pretty evenly for a while with Moody making two free throws to tie the game at 43 with 13:06 left. The Rebels then broke the game open with a 12-3 run, triggered by back-to-back 3-pointers by White to bolt out to a 55-46 lead.
"I thought Alabama's zone in the first half had us really perimeter oriented and had us very stagnant. We were settling for way too many jump shots," Mississippi coach Andy Kennedy said. "In the second half we played with much better rhythm. We made some adjustments. In the second half we were able to create some driving lanes with our spacing. I thought we made some key plays down the stretch."
"It was a combination of our turn-overs and them doing what they do," Alabama coach Anthony Grant said. "Moody's a tough cover. White is more than a capable scorer. Those two guys and us committing nine turnovers in the second half gave them opportunities to get out and get easy scores."
Randolph said when Mississippi went on its run that Alabama didn't answer. "We always talk about basketball as a game of runs," he said. "We have to be able to withstand their runs. You just have to keep fighting. It's a 40-minute game. They made their run and we weren't able to respond to their run."
Playing in their last regular season home game, Cooper and Randolph got Alabama off to a fast start. Cooper scored the first five points of the game on a 3-point shot and two free throws and Randolph canned a three-pointer at the 16:44 mark to give the Crimson Tide an 8-0 lead. Mississippi went on a 22-14 run to tie the game 22-22 on a basket by Sebastian Saiz with 5:24 left. Alabama then outscored the Rebels eight to two before White buried a 3-point shot with :02 to go to make it 30-27 at the half.
Crimson Tide: It was Senior Night for Alabama with 1,000 point-plus scorers Levi Randolph and Rodney Cooper as well as walk-on Dakota Slaughter playing their last regular season game at Coleman Coliseum. . Randolph is the first Academic All-American in Alabama basketball history. . Anthony Grant coached in his 200th game at Alabama and needs 8 more victories to reach 200 wins. . Five of Alabama's 12 losses, including four in SEC play, have come down to the final possession. . Alabama has lost two of its top four scorers, junior guard Ricky Tarrant and sophomore forward Shannon Hale, for the remainder of the season due to injury.
Rebels: Ole Miss entered the game on a two-game losing streak but at 11-6 in SEC play remains in the hunt for an NCAA Tournament berth. . Stefan Moody came into the contest leading the SEC in free throw shooting percentage (91.2) and was fourth in the league in scoring. . Mississippi entered the game 4th in the nation in free throw percentage (77.6. . Ole Miss has 36 wins in SEC play in the last three years, trailing only Florida and Kentucky.
Crimson Tide: With 1,598 wins entering the game Alabama needed two more victories to become the 34th school in Division I to reach the 1,600 win plateau. . Randolph's 32 points enabled him to move into 28th place on the school's all-time scoring list. . With 131 games played Randolph needs four more games to become the school's all-time leader in games played with 134. . Rodney Cooper needs 4 more rebounds to reach the 500 mark in his career.
Rebels: Jarvis Summers is tied for the active SEC career leader in points (1,580), assists (500), minutes (3,730) and wins (82) and is just the 5th player in SEC history with 1,500 points and 500 assists. . Summers' 500 career assists ranks second in school history.
Crimson Tide: At Texas A&M on Saturday.
Rebels: Host Vanderbilt on Saturday.
AP: Ole Miss 82, Alabama 74
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