Barrett connected five times from 3-point range for the Tigers (6-7), who were 6-for-8 behind the arc in the first half and led 41-32 at the break.
Hummer scored 16 first-half points, and the senior forward moved into seventh place on Princeton's career scoring list with 1,381, passing Bob Scrabis (1985-89). Hummer made 10 of 16 shots in the game.
Jack Isenbarger scored 16 points and Lucas Troutman 14 to pace Elon (8-6), which never led. The Phoenix won 56-55 at Princeton last season and had beaten their two previous Ivy League opponents this season, Dartmouth and Columbia.
Isenbarger made two 3-pointers to move into a tie for fifth with Chris Long (2007-11) on Elon's career list with 172.
With a trio a top recruits from Philadelphia, the Penn State basketball program is primed to finally turn a corner.
Maryland point guard Melo Trimble, considered a lock to leave the program before struggling in the second half last season, has withdrawn from the NBA draft and will return for his junior season.
Louisville's Chinanu Onuaku, who recently underwent a medical procedure to correct a heart rhythm issue detected during the combine, will keep his name in the NBA draft pool.