The Ukrainian is brimming with confidence after winning the Strasbourg title last month following her maternity break and is quickly rediscovering the form that took her to the last eight in Paris in 2015, 2017 and 2020.
She began brightly on a shadowy Court Suzanne Lenglen to bag two early breaks before handing one straight back to Kasatkina, but she ensured that was the only blip in the 45 minutes she took to wrap up the first set.
Svitolina, who is married to French player Gael Monfils (38) and enjoys huge support among local fans, roared back from 2-0 down in the second set with both players struggling to hold serve and got her nose in front with some heavy hitting late on.
"I definitely wouldn't have dreamt of this when I was giving birth," said Svitolina, whose daughter Skai was born in October. "It's unbelievable to be able to compete.
"And going all the way to the quarter-finals is a special feeling. I hope I can push even further, I'm really motivated for the next few matches."
With popular Russian singer Zemfira - an opponent of Moscow's invasion of Ukraine - watching from Kasatkina's box, Svitolina squandered a match point and got pulled into a tie-break where the pressure mounted.
But the Ukrainian settled her nerves to wrap up the contest and, while there was no handshake, Kasatkina gave her opponent a thumbs-up before walking away.
In the quarter-finals, Svitolina will take on world number two Aryna Sabalenka (25) or 2017 US Open champion Sloane Stephens (30) who meet in the night session later.
