Duke (6-5, 4-3 Atlantic Coast Conference) made 7 of 10 foul shots in the last 79 seconds after Khalid Moore's layup with 1:40 left pulled Georgia Tech into a tie at 68.
Matthew Hurt's 3-pointer with 18:40 to play gave Duke its largest lead at 38-27. The Yellow Jackets proceeded to outscore Duke 25-14 over the next 10 minutes and tied it at 52 on Jordan Usher's layup with 9:30 left.
Duke closed the first half with a 10-0 run and went to intermission with a 33-25 lead. After Mark Williams threw down a dunk to tie it at 25 with 3:37 before the break, Steward made two foul shots and sank a pair of 3-pointers. Georgia Tech missed its last five shot attempts and committed four turnovers in the last four minutes.
Hurt scored 17 points and Jordan Goldwire had 11 for Duke.
Jose Alvarado scored 26 points on 10-for-15 shooting for Georgia Tech (7-5, 3-3). Moses Wright added 12 points with 14 rebounds.
Georgia Tech hasn't won at Cameron Indoor Stadium since 2004.
The Blue Devils entered Tuesday's game with the fewest number of wins in their first 10 contests since the 1982-83 season. The 1994-95 squad was the last time a Blue Devils team finished below .500 going 13-18.
Georgia Tech returns home to face 16th-ranked Florida State on Saturday. The Blue Devils, with six of their next nine games at home, host Clemson on Saturday.
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Johnson's clutch and-1 helps Duke snap 3-game skid
Blue Devils freshman Jalen Johnson spins for an and-1 bucket to give Duke a lead in the final minutes.