Parker converted 6-of-12 shots from the field for the Blue Devils (21-5, 10-3 ACC), who have won four in a row and committed just five turnovers to a dozen for Georgia Tech (13-13, 4-9).
Rodney Hood contributed 14 points for Duke and Rasheed Sulaimon scored 11.
Georgia Tech was led by Robert Carter's 13 points. Kammeon Holsey scored a dozen, but the Yellow Jackets shot 39.1 percent from the field and 33 percent from 3-point range en route to their third loss in four starts.
Duke took control of the contest in the first half by outscoring their hosts 43-27.