Kerber, who kicked off her 2019 campaign with four consecutive singles match wins at the Hopman Cup last week, struggled on her return to Sydney and landed only 44 percent of her first serves in the first set.
Giorgi took her opportunities and leapt to a 3-1 lead, but four consecutive backhand errors meant she lost her advantage as her German opponent broke back immediately.
Kvitova overcomes Barty to take Sydney International title
As Kerber gradually tightened up her game, Giorgi stumbled, making two double faults and three unforced errors to concede the opening set in a tiebreak.
Giorgi responded with an early break in the second set, but Kerber asserted her status as one of the most aggressive players on the tour, racing through the final five games to seal the win.
Kerber will face two-time Wimbledon champion Petra Kvitova or Taiwan's Hsieh Su-Wei for a place in the semi-finals.
Local favourite Ashleigh Barty set up a pre-Australian Open showdown with world number one Simona Halep after beating 2017 French Open champion Jelena Ostapenko 6-3 6-3.
World number 15 Barty, who finished runner-up last year, converted five break point opportunities and won 85 percent of points on her first serve to seal her progress to the last 16.
"The ultimate goal is to go top 10. I'd love to go deep in a major, and hopefully I can do it here in Australia," Barty said after recording her third win from four outings this season.
"I feel like I have played enough matches now, I'm ready, feel pretty good on the court. There's certainly no better challenge than coming up against Simona right before a Slam."
Former world number one Garbine Muguruza withdrew from the tournament ahead of her second-round encounter with seventh seed Kiki Bertens, due to a gastrointestinal illness.
Dutchwoman Bertens will next meet American Sloane Stephens or Kazakh Yulia Putintseva in the quarter-finals.
Halep stunned by Barty in Sydney second round
Muguruza withdraws from Sydney event