Svitolina produced a superb fightback to upset last year’s finalist Paolini, saving three match points before winning the second set and taking control in the third.
Italian Paolini had a breakthrough year in 2024, reaching the French Open and Wimbledon finals and was regarded a title contender in Paris.
The 29-year-old came into the tournament in good form after winning the Italian Open last month, and started well, taking the opening three games.
After the pair traded breaks, Paolini pummelled a forehand winner past Svitolina for the decisive one to take the first set 6-4.
As both struggled to hold in the second set, the Italian served at 5-3, but Svitolina saved two match points and forced a tie-break.
The 30-year-old held off another match point in the tie-break before winning the set and taking that momentum into the deciding third set.
Svitolina dominated with her forehand, hitting 10 winners to Paolini’s four, before a backhand down the line secured her place in the last eight for a fifth time at Roland Garros.
“I still cannot believe this match finished my way. I still feel my head is in the match and in a big battle,” she said.
“It was a really difficult match, Jasmine was playing really well. It was tough for me but I’m happy I stayed composed, fought until the very last point and here I am in the next round.”
Meanwhile, 16th seed Anisimova had enjoyed success against Sabalenka in the past – winning five of their previous seven matches – but this time the Belarusian proved too strong as she clinched victory in straight sets.
Sabalenka’s power was on show throughout, firing down 11 aces, and while Anisimova made her work at times – not least by saving seven match points – she would not be denied.
“I’m super hungry for this tournament,” said Sabalenka, who will play Chinese eighth seed Zheng Qinwen next after the Olympic champion beat Russian Liudmila Samsonova 7-6 (7-5) 1-6 6-3.
“I love this place and I want to stay here until the very last day.”