Strong on serve, the world number two broke twice in the opening set and raced to a 3-0 lead in the second on a sunbathed court Philippe Chatrier to set up a meeting with American Sloane Stephens (30) or Yulia Putintseva (28) of Kazakhstan.
Sabalenka, who beat world number one Iga Swiatek (21) in the Madrid Open final last month, has yet to lose a set in the tournament and has now broken her third-round loss streak in Paris.
The Belarusian, whose run at Roland Garros was stopped at that stage in the three previous editions, was always in control and despite some minor blips, faced only one break point - which she saved with a second-serve ace.
"It feels amazing to feel the support and just to be on this court and have the opportunity to play tennis," the Australian Open champion said after an encounter that lasted a little over an hour.
"Every tournament is different, Roland Garros is especially different from the Australian Open because of the surface but winning gives you confidence."
Check out the game summary with Flashscore.
Khachanov looked to be in trouble midway through his match against Kokkinakis but stepped up his game in the crunch moments to get past his Australian opponent 6-4 6-1 3-6 7-6(5).
World number three Jessica Pegula had never beaten Elise Mertens in two previous meetings and the American's hopes of snapping that run to remain on track for a maiden Grand Slam trophy ended in disappointment following a 6-1 6-3 defeat.
Pegula particularly struggled against the versatility of Mertens, who ran her opponent ragged with some delightful sliced forehands, drops, lobs and deep shots to breeze through the match in 82 minutes.
Daria Kasatkina was even quicker across the finish line against another American as the ninth seed dropped only one game in her win over Peyton Stearns.
"I have to be quick because I'm not that powerful like many girls," Kasatkina explained. "Physically I'm not that gifted, so I have to be quick. I have to find ways to win, to survive.
"So I have to do it with my legs, with the brain, and try to squeeze the maximum I can."
Last year's semi-finalist Kasatkina will need to show her best form again in the next round where she can potentially meet former world number three Elina Svitolina. The Ukrainian takes on Russian Anna Blinkova later on Friday.
Anastasia Pavlyuchenkova, the 2021 runner-up, got off to a slow start before finishing strong to down 24th seed Anastasia Potapova 4-6 6-3 6-0 to book a clash with Mertens.
Novak Djokovic, who is seeking a 23rd Grand Slam title, is in action against Alejandro Davidovich Fokina while world number one Carlos Alcaraz will play Denis Shapovalov in the evening session.
