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.
Notable deaths of 2014 [PHOTOS]