Jason Morris added 13 points for the Yellow Jackets (12-17, 4-11 Atlantic Coast Conference), who pulled away from a seven-point halftime lead to snap an eight-game conference losing streak.
The loss also continued Wake Forest's season of frustration under first-year head coach Jeff Bzdelik, who replaced Dino Gaudio after three winning seasons and two trips to the NCAA tournament.
Already assured of its worst record since 1985-86 -- going 8-21 in then-head coach Bob Staak's first season -- the Demon Deacons also posted their worst ACC record since 1986-87 (2-12).
With two of the league's worst teams on the court -- Georgia Tech's RPI was 182nd coming in, Wake Forest's 246th -- both sides had their problems Thursday.
For the Yellow Jackets, it was fouls -- 24 in all, with Shumpert spending more than 10 minutes of the first half on the bench after getting two fouls, and Mfon Udofia fouling out early in the second half.
But the Demon Deacons had trouble with Georgia Tech's defense, committing 22 turnovers (19 off steals), shooting 32.6 percent from the field and being outrebounded 44-27.
Still, Wake Forest managed to lead by as many as five points twice in the first eight minutes of the first half, the last at 18-13 on Tony Chennault's layup with 12:13 remaining.
But the Yellow Jackets fought back, holding the Demon Deacons without a field goal for more than six minutes during a 17-0 run. Jason Morris hit a 3-pointer with 10:29 left to tie the score at 18-18, then Shumpert's layup with 4:40 remaining put Georgia Tech up 32-20.
Wake Forest rallied, pulling within 32-28 on Harris' layup with 1:47 left, but Miller's 3-point play 33 seconds later gave the Yellow Jackets a 35-28 lead at the halftime break.
Another shooting drought by the Demon Deacons in the opening minutes of the second half allowed Georgia Tech to take command.
The Yellow Jackets held Wake Forest without a field goal for nearly seven minutes, extending their lead past the 20-point mark on Lance Storrs' 3-pointer with 16:39 left.
The Demon Deacons would pull no closer than 15 points the rest of the way, while Georgia Tech would extend its lead to 28 points (76-48) on Morris' layup with 2:53 remaining.