Davis, who entered the game averaging 19 points and 10 rebounds, finished with 17 points and tied a season-high with 16 rebounds. Rocky Tarrant added 11 points.
Tulane (5-2) opened the game on a 17-4 run, led by five apiece from Tarrant and Davis. The Green Wave, who outshot Loyola 46.2 percent (18 of 39) to 29.2 percent (7 of 24) in the first half, led by as much as 23, 36-13, before taking a 44-21 lead into intermission.
Loyola (5-4) bounced back after the break, shooting 51.6 percent (16 of 31) and holding Tulane to 28.6 percent (8 of 28), but Tulane made 11 of 14 free throws to put the game away.
Kyle Simmons led Loyola with 15 points.
Colorado State graduate transfer John Gillon has chosen Syracuse, giving the Orange a potential starter at point guard entering the 2016-17 season.
DeSean Murray, who averaged 20.2 points as a sophomore at Presbyterian, will transfer to Auburn to play for coach Bruce Pearl.
Former Kentucky guard Ed Davender, the only Wildcat with at least 1,500 points and 400 assists, has died. He was 49.