Florida (16-4, 4-1 Southeastern Conference) fell behind 20-4 in the opening minutes and trailed 38-28 at halftime. But the Gators worked their way back thanks to lockdown defense and clutch 3-pointers from Boynton and Mike Rosario.
Young was 7 of 10 from the field despite playing on with tendinitis in his right ankle. Erving Walker had 10 points and nine assists.
Terrance Henry had 21 points for Ole Miss (13-7, 3-3), while Nick Williams added 14. The Rebels shot 60.9 percent from the field in the first half, hitting all six of their 3-point attempts. They couldn't duplicate that success in the second half, making just 8 of 29 (27.6 percent) from the field.
Ole Miss got the pace it wanted from the very beginning, forcing Florida into a half-court, physical game. That negated the Gators' one major strength — superior guard play — and they struggled to find open 3-point looks for much of the game.
The Rebels went on a 14-0 run to take a 20-4 lead in the first 8 minutes before settling for the 10-point halftime lead. They made 14 of 23 shots from the field in the first half, and had an uncharacteristic good touch from long range. Williams hit four of the team's six 3-pointers, knocking the Gators on their heels.
Ole Miss came into the game as the worst 3-point shooting team in the SEC, making just 27.2 percent.
But Florida slowly climbed back into the game in the second half behind Young and some well-timed 3-pointers, including Scottie Wilbekin's with 10:11 remaining that tied the game at 46. Young's dunk gave the Gators a 48-46 lead — their first since the opening minutes.
While Florida was heating up, the Ole Miss offense was grinding to a halt and the 3-point shooting reverted to previous form. The Rebels scored only eight points in the first 12 minutes of the second half.
Rosario put the Gators ahead for good with 5:29 remaining, draining a 3-pointer for a 53-52 lead. Boynton gave Florida some separation minutes later, hitting consecutive 3-pointers to push the lead to 59-54.
Ole Miss pulled within 63-60 with 18 seconds remaining and had a chance to tie. But Florida's defense slapped the ball away from Marcus Aniefiok, who was trying to find room to take a 3-pointer, and Bradley Beal hit a free throw that sealed the victory.
The Gators have won six of their past seven games.
Read more in Friday's NEMS Daily Journal newspaper.