The Gators (19-8, 8-4 Southeastern Conference) converted a season-best 25 of 27 free throws, 93 percent, to earn the edge in a battle of teams on the NCAA Tournament bubble. Chandler Parsons scored 13 points and Walker added 10 for Florida.
Terrance Henry led Ole Miss (17-9, 5-7) with 17 points and Chris Warren had 14 points. The Rebels, who were ranked No. 14 in mid-January, have lost five of their last six contests.
Ole Miss held a 56-54 lead with 2:24 left on a three-point shot by Terrico White, but managed only one basket the rest of the way. Florida tied it on a pair of free throws by Parsons, setting up the decisive play.
Florida took a 58-56 lead with 58 seconds left on Kenny Boynton's layup after a steal by Alex Tyus. The Gators closed it out on their final three possessions as Walker converted six free throws.
Terrico White missed a potential game-tying 3-point shot at the buzzer.
Florida enhanced their NCAA Tournament resume, completing a 6-0 sweep against SEC Western Division teams. The Gators have won four their last six starts and improved to 5-1 in games decided by five points or less.
Florida shot 37 percent from the floor (19-for-52) and 1 of 13 from 3-point range. The Gators did compensate for their woeful shooting by making their foul shots and forcing 15 turnovers.
Ole Miss was 23 of 55 from the field (42 percent) and 6 of 20 from the 3-point line. The Rebels were 9 of 11 from the free throw line and out rebounded Florida 36-30.
Read more in the Sunday NEMS Daily Journal newspaper. Click here for more at Parrish Alford's blog.