Parker put in 11 of his points in the second half for the Blue Devils (22-6, 11-4 ACC), who dealt the Orange a second straight tough loss after Syracuse had run its season record to 25-0.
Quinn Cook put the game away with three free throws, awarded when Syracuse Coach Jim Boeheim drew a pair of technical fouls and was thrown out of the game with 10.4 seconds remaining.
Boeheim -- incensed when C.J. Fair was whistled for an offensive foul while converting a layup that would have tied the score 60-60 -- charged onto the court to confront the officiating crew.
Rodney Hood added 13 points for Duke.
Jerami Grant totaled 17 points with eight rebounds and Fair finished with 12 and seven for the Orange (25-2, 12-2), who had previously fallen in a shocking upset to Boston College Wednesday.