Rasheed Sulaimon added 19 points for the Blue Devils (18-5, 7-3 Atlantic Coast Conference).
They shot nearly 51 percent, hit 12 3-pointers against one of the ACC's best perimeter defenses and used a big run at the end of the first half to roll to their eighth straight victory over their instate rivals.
Devin Thomas had 14 points before fouling out for the Demon Deacons (14-9, 4-6), who have lost three straight for the first time this season.
They had 19 turnovers — including five straight during Duke's decisive run.
Playing without leading scorer Codi Miller-McIntyre, Wake Forest hung around for about 15 minutes before ultimately losing their 15th straight at Cameron Indoor Stadium — all by double figures.
Andre Dawkins added 17 points with four 3-pointers for Duke, which won its 29th straight home game — tied for the longest active streak in the nation with No. 3 Florida, which beat Missouri earlier Tuesday night.
Parker reached the 20-point mark for the 13th time and third time in ACC play.
Playing their first game since their thrill-a-minute, 81-79 overtime loss at eventual No. 1 Syracuse, the Blue Devils showed no signs of a hangover. Duke improved to 24-1 after a loss since the start of 2009-10, and was never really in danger of its first consecutive defeats since the 2012 ACC and NCAA tournaments.
The Blue Devils did it this time with defense, with pesky guard Tyler Thornton recording three of the team's 10 steals — and receiving an enthusiastic high-five from coach Mike Krzyzewski after deflecting another ball out of bounds.
Duke scored 26 points off all those Wake Forest giveaways.
Arnaud William Adala Moto had 10 points and 10 rebounds, and freshman Miles Overton had a season-high 12 points for the Demon Deacons, who fell to 2-28 in ACC road games under fourth-year coach Jeff Bzdelik.
Miller-McIntyre, who averages 14.4 points, was in uniform on the bench but was unable to play after spraining his ankle three days earlier against Georgia Tech.
Even without him, Wake Forest managed to keep this one competitive for a little while.
And then it got out of hand in a hurry.
Duke held Wake Forest without a field goal for more than 7 minutes late in the first half and used an 18-1 run to first take the lead for good, then push it well into double figures.
The Blue Devils — who shoot 3-pointers at an ACC-leading 41 percent clip — hit four 3s in roughly 3½ minutes during that run, including two by Rodney Hood about 30 seconds apart. Sulaimon closed the run by hitting from long range with about a minute left before the break to make it 44-29.