The Blue Devils went 2-3 under interim coach Ted Roof , who will be interviewed for the full-time job with several other candidates.
Douglas has thrived under Roof, getting four of his six 100-yard games this season to tie a school record.
Meanwhile, the loss left North Carolina (2-10, 1-7) with its worst record since going 1-10 in '89.
The Blue Devils took control of the clock from the start, keeping North Carolina's defense, one of the nation's worst, on the field for more than 21 minutes of the first half. Duke outgained North Carolina 283-39 in the opening half.
A 45-yard run by Douglas set up the first of three Duke field goals and Dargan scored on a pair of 1-yard runs in front of stunned crowd at Kenan Stadium, many of whom booed after each failed drive by the Tar Heels.
And while the Duke QBs were sharp, Darian Durant had his worst half of the season as North Carolina managed just one first down.
North Carolina had a chance to score late in the second quarter when Michael Waddell's 63-yard kickoff return set up Durant at the Duke 34. But three incomplete passes and a penalty ended the threat.
Durant rebounded to have a stellar second half, throwing for two scores and running for another, twice getting his team within one score of a tie.
But the Tar Heels failed to pick up a first down after getting the ball back with 2:36 left and Duke ran out the clock.
The last time Duke won as many as four games in a season was 1998 when Fred Goldsmith led the Blue Devils to a 4-7 record.