Davis was coming off a career-high 35 points against Marshall earlier in the week, and had another spectacular performance on Saturday, shooting 9 of 15 from the field and 12 of 12 on free throws.
His 3-pointer with 2:11 remaining stopped a final Central Florida rally. Davis is averaging 28 points over his past four games.
Southern Miss (23-8, 12-4 Conference USA) has secured the second seed in next week's league tournament. The Golden Eagles have won five of their past seven games.
Central Florida (20-11, 9-7) ends its season with the loss. The Knights are ineligible for the postseason because of NCAA sanctions. Isaiah Sykes led UCF with 22 points.