"We're going to ACC play the way we want to go," Okafor said.
Quinn Cook had 15 for the Blue Devils (12-0), who shot nearly 56 percent -- 71 percent in the second half.
They broke open a tight game by outscoring Wofford 43-21 in the final 20 minutes, including the final 13 points.
Okafor was 11 of 13 from the field while reaching the 20-point mark for the fifth time in seven games, and all 16 of Winslow's points came during a tight first half.
Karl Cochran had 13 points for the Terriers (9-4) on 5-of-17 shooting.
They shot 38 percent and kept it close well into the second half but went nearly 5 critical minutes between field goals while fading for their second straight loss. Both have come on the home floors of nationally ranked opponents.
"I can't say there have been many times in my career when we got our fannies whipped by 29 or whatever it was, and I was proud," Wofford coach Mike Young said. "My guys stuck it up there and battled against an obviously very good basketball team."
Before Atlantic Coast Conference play begins this weekend, coach Mike Krzyzewski wanted his talented but young team to face a test from a one-two punch of mid-majors with strong profiles. Less than 48 hours earlier, Duke beat Mid-American Conference favorite Toledo 86-69.
"These two games have really gotten us in conference mode," Krzyzewski said.
And just as in that one, it took a while for the Blue Devils to finally pull away.
Okafor scored seven points during a 22-12 run during the first 9 1/2 minutes of the half. He started it with a layup on Duke's second trip down court after the break, and Cook followed that with a 3-pointer that pushed the lead into double figures for the first time at 46-34.
Amile Jefferson capped the run with a layup that made it 63-45 with 10 1/2 minutes remaining.
Reigning Southern Conference champion Wofford had been off since a 33-point loss at No. 17 West Virginia on Dec. 22, but already won once at a venerable ACC venue, claiming a one-point win over North Carolina State at Reynolds Coliseum on Dec. 14.
For the first half anyway, the Terriers looked plenty capable of stunning the Blue Devils: Wofford led for just under a minute of the half and Duke never led by more than eight.
STAT SHEET The Blue Devils trailed for 54 seconds of the first half, bringing the total amount of time they have trailed all season to 5 minutes, 55 seconds. Cochran's 3 with 10:57 left in the first half put Wofford up 15-14, before Jefferson put the Blue Devils back on top to stay with two free throws with 10:03 to go.
QUOTE OF THE DAY Krzyzewski said he broke his watch's wristband while slapping the floor during the Toledo game, and he was asked if he owned more than one watch. After replying that he does, he added: "I'm not boasting, but I have a lot of rings, too."
TIP-INS Duke: The Blue Devils wrapped up the home non conference schedule with their 116th straight win in non-ACC games at Cameron Indoor Stadium.
Wofford: The Terriers are 0-21 against nationally ranked opponents.