Rasheed Sulaimon added 10 points for the Blue Devils (19-5, 8-3 Atlantic Coast Conference). Parker extended his Duke freshman record to 14 games with 20 points or more.
The Blue Devils put it away with an 18-0 run midway through the second half, improving to 18-2 against unranked teams this season.
Following a solid first half, Parker scored 12 of Duke's initial 17 points after halftime as the Blue Devils opened a 56-44 lead on his three-point play with just under 14 minutes to go.
He had a baseline jam on the first possession and followed that with a three-point play when he was fouled on a fast-break layup, pushing Duke's lead to 44-35. He added a fast-break dunk, two free throws and another three-point play.
Following Anderson's free throw that cut it to 44-38, Sulaimon nailed a 3 from the right wing, giving the Blue Devils their first double-digit lead.
When it wasn't Parker for the Blue Devils, on pace to finish with the third-best 3-point shooting mark in school history, it was Cook, Rodney Hood or Sulaimon nailing 3s. Cook's made it 64-44 with just under 11 minutes left.
Parker had a two-handed slam with 5:10 to play and was whistled for a technical for hanging on the rim too long, bringing a smattering of boos from the crowd.
The Blue Devils led 39-35 at halftime.
Parker, who entered second in the ACC in scoring (18.7 points per game) and leading the conference in rebounding (8.2), proved to be as tough as expected for Boston College to handle in the first half when he compiled 10 points and seven rebounds.
There were a large number of Duke fans and, very likely, a good number of Boston Celtics fans interested in getting a live look at Parker as the local NBA franchise looks to rebuild quickly through the draft after dealing veteran stars Paul Pierce and Kevin Garnett to Brooklyn last summer. Celtics President of Basketball Operations Danny Ainge was seated courtside.
The Eagles tried several things in trying to slow Parker in the opening half. They switched defenses three times in the opening 10 minutes, going from man-to-man to zone and even using a box-and-1 at one point. They had guards attempting to play in front of him, forcing lob passes over the top, and had forwards covering him straight up. Still, his 6-foot-8 frame and quickness were on display whenever he got the ball.
The Blue Devils nailed three from beyond the arc, pulling to an 11-4 edge in the initial 4:15 before BC started driving to the basket, getting easier shots and setting up open jumpers. The Eagles scored 12 of the next 17 points, tying it at 16 on Alex Dragicevich's 3-pointer from the right wing.
Neither team held more than a one-possession lead the rest of a half. Both shot 50 percent on 3s in the opening 20 minutes.