Entering the game with a chance to become the career leading scorer in the Atlantic Coast Conference, Redick missed 15 of his first 17 shots, but he did hit the go-ahead jumper with 8:51 remaining.
Redick needs nine points to break the ACC mark of 2,587 set by Wake Forest's Dickie Hemric 51 years ago. The Blue Devils' next game is Saturday in Philadelphia against Temple.
Duke (26-1, 14-0) has won 20 of 21 games against Georgia Tech since losing in Atlanta 10 years ago. The Yellow Jackets (10-15, 3-11) have lost three straight overall and are 1-11 since beating Centenary last month.
Williams kept the Blue Devils close with an eight-point barrage after Jeremis Smith layup gave Georgia Tech an 11-point lead 1:31 into the second half. A putback of Redick's missed 3-pointer cut the lead to eight before Williams took Greg Paulus' bounce pass and jammed to bring Duke within two with 14:07 to go.
The signature moment came when freshman forward Josh McRoberts stole a pass and dribbled twice behind his back as he drove past the halfcourt line. Seeing Redick coming up the right side, McRoberts fed the senior guard, who buried an 18-footer to give Duke a 55-53 lead it never relinquished.
Redick, the NCAA's career leader in 3-pointers, hit a 25-footer on the next possession and followed that with two free throws that ended a 24-6 run. Georgia Tech missed nine of 12 shots and committed nine turnovers during the stretch that spanned 12:02.
Smith finished with 18 points and 12 rebounds, while Ra'Sean Dickey added 14 points and Zam Frederick had nine assists.
Duke's Mike Krzyzewski passed Phog Allen of for 11th place on the career coaching list with his 747th victory. Krzyzewski improved to 42-16 against Tech overall and 105-9 against unranked ACC teams over the last nine years.
Yellow Jackets coach Paul Hewitt dropped to 1-12 against the Blue Devils.