Giorgi moved into the fourth round with a 4-6 6-1 6-0 defeat of the seventh seed on Court Simonne-Mathieu.
Italian Giorgi broke the two-time grand slam semi-finalist from Belarus’ serve six times as she booked a meeting with Daria Kasatkina, progressing beyond the third round for the first time at Roland Garros.
Veronika Kudermetova earlier reached the last 16 of a major for the first time when Paula Badosa retired from their third-round match due to a right calf injury at 6-3 2-1 down.
With third seed Padosa and Sabalenka making an exit, world number one Swiatek is an even stronger favourite to win the title for the second time.
The top seed saw off Danka Kovinic 6-3 7-5 in the opening match of the day on Court Philippe-Chatrier.
It is only the second time this century that only one of the top-10 seeds has reached the fourth round, with the other occasion being when Karolina Pliskova was the last such player left standing at Wimbledon four years ago.
Czech Pliskova failed to capitalise at the All England Club, as she was knocked out in the fourth round.
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