Zion Williamson added 22 points to help the Blue Devils (17-2, 6-1 Atlantic Coast Conference) win their third straight and 12th in a row in the series with Georgia Tech.
Duke finished a season-worst 2 of 21 from 3-point range but hit 52 percent from the field in the second half to win its lowest-scoring game of the year.
Abdoulaye Gueye had 14 points and Michael Devoe added 11 for the Yellow Jackets (11-9, 3-4), who have lost four of six but threw a scare into Duke for most of the day. Georgia Tech led 38-31 when Gueye banked in a jumper with just under 16 minutes remaining.
The Blue Devils countered with a 21-4 burst keyed by eight straight points from Barrett and capped by a layup from Williamson that made it 52-42 with just under eight minutes remaining.