Parker scored 16 points during the opening 20 minutes while the Blue Devils were building a 20-point lead. He was one of four members of the Blue Devils to reach 20 points for the game.
Duke opened its season by hitting 70 percent from the field, making 13-of-21 from 3-point range and turning the ball over just four times.
Parker finished with 22 points, as did Rodney Hood. Quinn Cook added 21 for the Blue Devils and Rasheed Sulaimon had 20.
De'Mon Brooks scored 24 points to lead Davidson, which attempted 21 shots from beyond the arc and made just three of them.