Frantz Massenat chipped in with 14 points and six assists for Drexel (4-7).
After trailing at halftime 34-28, Nik Cochran made two free throws with 3:12 left in the second half to bring Davidson (6-5) within four, 57-53.
Four points would be the closest the Wildcats would get, as Drexel closed out the game on an 11-5 run. Lee sparked the run with a layup at the 2:21 mark, then made a dunk and converted on four free throws down the stretch to seal the victory for the Dragons.
Drexel dominated on the boards, outrebounding Davidson 40-14.
De’Mon Brooks finished with 16 points to lead Davidson in scoring. Cochran and Jake Cohen added 10 points apiece for the Wildcats.