Kyle Singler added 13 points and Greg Paulus had 11 to help the Blue Devils (24-3, 11-2) improve to 15-0 at Cameron Indoor Stadium this season and win their second straight since a two-game losing streak on the road.
Matt Causey and Gani Lawal had 10 points each to lead the Yellow Jackets (11-15, 4-8), who lost their fifth straight and were denied their first victory at Cameron since 2004. Duke has won 10 of the past 11 meetings here.
Georgia Tech's leading scorer, Anthony Morrow - who entered averaging 14.3 points - was held to nine on 4-of-9 shooting.
Duke never trailed in the second half and led by double figures for most of the way, but the Yellow Jackets briefly made things interesting when Morrow's 3 with 2:40 remaining pulled them to 65-57. About 30 seconds later, Nelson threw a pretty bounce pass to Henderson, who finished the layup that restored their double-figure advantage.
The perimeter-oriented Blue Devils led 33-27 at halftime despite some horrible shooting from the outside. Duke, a 39 percent shooting team from 3-point range, made just two jump shots in the half and was 1-of-11 from beyond the arc.
Duke missed 12 of its first 13 attempts from 3-point range before Paulus connected from the key with 9 minutes to play to give the Blue Devils a 56-44 lead. They finished just 2-of-15 from long range.
Meanwhile, Georgia Tech had serious trouble getting to the free-throw line. The Yellow Jackets didn't attempt a foul shot until Causey sank two with 9½ minutes left after he was hammered by Paulus while driving, and finished 7-of-11 from the line.