Two of Davis' scores came in the fourth quarter and matched the two touchdown passes thrown by Jeremiah Masoli as Ole Miss tried to rally.
Arkansas (5-2, 2-2 SEC) had Ryan Mallett back at quarterback after he had been forced out of last week's loss to Auburn. Mallett was 13-of-24 for 210 yards Saturday.
Masoli was 21-of-36 for 326 yards and two touchdowns for Ole Miss (3-4, 1-3). He also ran for 89 yards.
The Razorbacks jumped out to a 21-0 lead in the second quarter and nearly shut the Rebels out in the first half except for a 22-yard field goal by Bryson Rose with 1:40 to play.
Ole Miss made it 24-10 in the third quarter on a Masoli's 18-yard TD pass to Ja-Mes Logan, but could do no more than trade touchdowns with their hosts in the final period.
The game in Fayetteville was delayed twice due to lightning in the area.