Barford, a first-team All-SEC selection, was 6 of 11 from the field and had a key 3-pointer and fast-break layup in the closing minutes. Should Arkansas defeat Florida, the Hogs would play the victor of Tennessee-Mississippi State game at approximately 2:30 p.m. on Saturday.
Three Ole Miss players scored in double-figures, including Terence Davis with 16 points, Stevens with 15 and Deandre Burnett with 13.
Arkansas trailed for the first 19:05, but with 4:51 to play in the first half the Gators hit a wall - a big part of it because Arkansas' perimeter defense had stepped up big time after a slow start. The Rebels fouled Frank Booker with 13.4 seconds remaining to send him to the free-throw line.
Florida hasn't reached the semifinals of the SEC Tournament since 2014, the year the Gators last won the event and made a run to the Final Four. Defensively, Arkansas yields 75.7 points per game against the opposing teams.
"I think we're slowly picking up steam and we're getting better", Arkansas coach Mike Anderson said.
Keith Stone led Florida with 22 points and finished 8 of 10 from the field.
Up next, the Hogs will have a quick turnaround with a tip against No. 2 Tennessee (23-7, 13-5 SEC) at approximately 2:30 p.m. (CST). The Gators maintained the lead, pushing it back to 29-22 at the 4:54 mark on a 3-pointer by Okauru.
The third-seeded Gators (20-11) will face sixth-seed Arkansas on Friday night in the SEC Tournament quarterfinals. The Tennessee Volunteers are shooting 37.7 percent from beyond the arc and 75.2 percent from the free throw line.
The win made it 40 victories in a row when Arkansas leads at halftime. As the horn sounded to end the game, Bruce Stevens drained a three-pointer from the corner.
Arkansas salted the game away at the free-throw line against a resilient Gamecocks squad that was led by Chris Silva with 15 points and 11 rebounds and Make Kotsar with 15 points and 11 rebounds. The 6-foot-7 Bailey was undersized against South Carolina's frontcourt for much of the night, but he scored nine points and had three steals and two blocks in 24 minutes - including a powerful dunk early in the second half.
Silva and Kotsar both scored 15 points to lead SC.
Arkansas entered Friday's SEC Tournament quarterfinal matchup with Florida 0-8 in games against the Gators since 2013. The Gators swept Auburn, Alabama and Kentucky down the stretch to pad their NCAA Tournament credentials and won the first and only matchup with Arkansas during the regular season 88-73 on January 17 in Gainesville. The game will be televised on SEC Network.