The Rebels (2-0) never trailed but couldn't pull away from the Colonels until late in the second half. A layup by Davis capped a 9-0 run that gave Ole Miss an 80-61 lead with 4:46 to play.
Rebels senior guard Deandre Burnett finished with 17 points and freshman Devontae Shuler added 12 points for Ole Miss.
Junior forward Nick Mayo had 19 points and 10 rebounds to lead the Colonels (1-1), who shot 51.0 percent from the field. Freshman guard Dedric Boyd also had 19 points on 6-of-17 shooting for Eastern Kentucky.
The game was a part of the MGM Resorts Main Event. Ole Miss will play Utah on Nov. 29 in a semifinal game the championship rounds of the tournament in Las Vegas.
Ole Miss led throughout the first half and was up 37-27 after five straight points from Davis with three minutes left before halftime. The Rebels went into halftime leading 40-34.
Ole Miss quickly pushed the lead back to double figures in the second half, with Dominick Olejniczak's dunk giving the Rebels a 51-40 advantage at the 16-minute mark.
Senior forward Marcanvis Hymon had a big all-around game for Ole Miss, scoring eight points and grabbing 10 rebounds with three assists and three blocks.
Ole Miss hosts Georgia State on Friday. Eastern Kentucky will try to bounce back Thursday when it hosts Kentucky State.