The 23-time grand slam champion had taken a break after losing to Bianca Andreescu at Flushing Meadows.

Having warmed up with a doubles win alongside Caroline Wozniacki on Monday, Williams was back in singles action on Tuesday and cruised past Giorgi 6-3 6-2 in a little over another hour.

"I thought it was solid, technically my second match of the year," she said.

"Spent a long time off from tournament play, match play, so solid is pretty good. It's a great start to build on.

"It's definitely not easy [to get the rhythm back]. It's always hard to play a match early in the season."

Williams will face Christina McHale next and could meet 15-year-old Coco Gauff for the first time in the quarter-finals.

Her doubles partner Wozniacki, who will retire after the Australian Open, also progressed having dropped just one game against Paige Mary Hourigan.

Former world No.1 and defending Australian Open champion Naomi Osaka had more difficulties in beating Maria Sakkari 6-2 6-7 (4-7) 6-3 at the Brisbane International.

Sakkari had the momentum in the decider when she forged an early break, yet Osaka fought back and converted her second match point after double faulting with her first.

Petra Kvitova and Kiki Bertens, who, like Osaka, started the new season ranked in the world's top 10, also advanced in three sets with respective wins against Anastasia Pavlyuchenkova and Dayana Yastremska, while Jennifer Brady came from a set down to oust Maria Sharapova.

Belinda Bencic was eliminated at the Shenzhen Open, though, the world No.8 and No.1 seed beaten 3-6 6-3 6-3 by Anna Blinkova.

Defending champion and No.2 seed Aryna Sabalenka was also knocked out as she suffered a straight-sets defeat to Kristyna Pliskova.