The win is the third in a row for the Razorbacks (5-2, 1-2 SEC) over the Rebels, who have now lost three of their first six games a season after winning the Sugar Bowl.
Austin Allen was 19-of-32 passing for 229 yards and three touchdowns for Arkansas, giving the junior an SEC-best 18 touchdown passes for the season. Rawleigh Williams added a career-high 180 yards rushing on 27 carries for the Razorbacks, who bounced back following a 49-30 loss at home to No. 1 Alabama a week ago.
"I told the guys, `Let's do whatever we have to do to protect this house," Arkansas coach Bret Bielema said. "They never wavered and needed help from the crowd, and they delivered."
Chad Kelly accounted for 342 yards of total offense for Ole Miss (3-3, 1-2), throwing for 253 yards and rushing for 89 more. The senior also threw for a touchdown and ran for two more.
Evan Engram led the Rebels with seven catches for 111 yards and a touchdown.
The two teams played an overtime thriller a year ago in Oxford , a game in which Arkansas completed a miraculous fourth-and-25 on its way to a 53-52 victory.
They also entered Saturday with the two most efficient quarterbacks in the SEC, and neither Kelly nor Allen disappointed. The duo combined for 571 yards of total offense.
It was Cornelius, however, who had the final say with his 6-yard touchdown run with 2:20 remaining.
Ole Miss had one more drive following Arkansas' go-ahead score, but Kelly fumbled on a fourth-and-16 scramble that came up short.
"We're in the games and competing," Rebels coach Hugh Freeze said. "We've got to see the big picture, even though it's hard to right now, sitting here."
Ole Miss: The Rebels entered the game 102nd in the country in total defense, allowing 449.4 yards per game. They once again struggled on Saturday by allowing 429 total yards to Arkansas, a number that was more than 450 before the Razorbacks purposely took several large losses while running out the clock on the game's final drive.
Arkansas: The Razorbacks still have offensive line concerns after allowing three more sacks of Allen, but they moved the ball consistently through the air and on the ground -- giving them renewed hope with only SEC games remaining this season.
Arkansas was in danger of falling out of the rankings, but now it's likely to once again push its way into the top 20 -- perhaps even surpassing the Rebels. The Razorbacks' only losses this season are to No. 1 Alabama and No. 6 Texas A&M.
Ole Miss: The Rebels are on the road for the second straight week, traveling to Baton Rouge to face LSU.
Arkansas: The Razorbacks play for the eighth straight week to open the season, traveling to No. 23 Auburn next week.