Buckner had 11 points, including his first 3-pointer of the season, 12 rebounds and eight blocks, which tied the school record set by Ansu Sesay in 1997.
"We went into the game saying we were going to play hard, start off with defense," Buckner said. "I know the team was motivated on my defense, so I played hard and it brought energy to the team. We came out and did the thing."
After Julysses Nobles tied the game at 43 for Arkansas, Ole Miss took control with a 17-4 run to go up 60-47 and never trailed again.
"Reg was tremendous," Ole Miss head coach Andy Kennedy, who became the fastest coach in program history to reach 100 wins, said.
"I thought he and Terrance (Henry) both gave us great presence both offensively and defensively at the basket. When we get Zach (Graham), when we get Reg, when we get Terrance, now we've manufactured enough points to give us a chance to win the game."
Ole Miss shot 45 percent (25-56) from the floor for the game, and outrebounded Arkansas by 14 (38-24). Ole Miss was 13 of 14 from the free throw line, good for 93 percent.
Graham had 17 points in the win. Henry had 11 and eight rebounds.
"Did a good job on the glass," Kennedy said. "We knew coming in one of the battles within the war was the glass. We had 14 offensive rebounds. We outrebounded them by nine, hold them to 36 percent (shooting) from the field. That, in essence, was the game. You hold a team to 60 in their own building, you like your chances."
Marshawn Powell led the Razorbacks (14-8, 4-5) with 19 points despite sitting out more than five minutes to start the game after injuring an ankle during the pregame shootaround.
Ole Miss next meets LSU at home Wednesday at 8 p.m.
"There can be no let up," Kennedy said. "Our next game is against LSU Wednesday night at home. I hope our home fans come out and support this team with energy in the building, which I know that they will. And maybe we can continue this."