The matchup of national powers played at Madison Square Garden was tied at the half, but the Blue Devils sprinted to a 12-point lead as the contest approached the midway point of the second period.
Parker scored eight of his 23 points during the opening 10 minutes of the second half, hitting a pair of 3-pointers during that stretch.
UCLA cut its deficit to less than 10 points on multiple occasions, but Duke then limited the Bruins to two points over the final three minutes to turn the game into a rout.
Quinn Cook and Rodney Hood both had 14 points for the Blue Devils (9-2). Duke tried 32 shots from 3-point range, almost half its field goal attempt total, and made 11 of them.
UCLA (9-2) was led by David Wear with 16 points and five rebounds.