The Orange remained unbeaten in their three games this season, pulling away in the second period after the Tigers had remained close through the first 26 minutes.
Princeton was within 45-39 when Christmas made his dunk with 13:23 to play in the contest and Syracuse then embarked on a 13-4 run.
James Southerland led the Orange off the bench with 22 points, hitting 7-of-11 shots from the field and all four of his free throw attempts.
C.J. Fair added 12 points while Christmas, Michael Carter-Williams and Brandon Triche all had 10.
Clay Wilson produced 13 points for the Tigers (1-3).
Syracuse recorded 19 steals and forced 24 turnovers overall.