Freshman Jon Scheyer added a career-high 18 points for the Blue Devils (9-1), who led the entire way to extend the nation's longest home nonconference winning streak to 48 games.
Will Thomas and Folarin Campbell each scored 13 points for the Patriots (4-4).
Nelson, who has been in double figures in all but one game this season, finished 8-for-10 from the field and hit two 3-pointers in the opening 4 1/2 minutes for the early lead. Scheyer _ a 6-foot-5 wing guard who had to play the point while Greg Paulus was sidelined in the preseason with a foot injury _ was 6-for-12 from the field, including four 3s, to better his previous high of 14 points against Davidson on Nov. 25.
They combined to score 29 of Duke's 36 second-half points, helping the Blue Devils build an 11-point halftime lead to as many as 18 points late.
Duke took control late in the first half with its defense, holding the Patriots without a point for almost the final six minutes. On the other end, the Blue Devils got a reverse layup from David McClure, a 3 from Paulus and a layup from Josh McRoberts to turn a 24-21 lead into a 33-22 halftime advantage.
The Blue Devils came out of the break with one of their best offensive surges of the season, getting seven straight points from Nelson and two 3s from Scheyer to make it 46-31 with 15:51 to play.
The Blue Devils have struggled with scoring and turnovers for much of the season with a young team, ranking last in the Atlantic Coast Conference at 68 points per game while averaging nearly 18 turnovers. But the Blue Devils did a much better job taking care of the ball, finishing with a season-low 11 turnovers while hitting a season-high nine 3-pointers.