Cohen was 8 of 14 from the field and made all seven of his free throws and Brooks was 8-of-12 shooting.
The Wildcats (24-7) outscored Elon 44-34 in the second half, shooting 51.9 percent (14 of 27) from the field. The Phoenix (15-16) shot 37 percent in the second half, missing all five of their 3-pointers.
Davidson scored 14 points off of eight Elon turnovers, while turning it over just five times.
Chris Czerapowicz added 12 points for the Wildcats, who play Western Carolina in the Southern Conference final on Monday.