The Belarusian player gave Stephens, the 2017 US Open champion, no hope at the start, unleashing a variety of hard shots that left Stephens, 30, stunned.
Sabalenka, the hardest-hitting player on the women's tour and the 2023 Australian Open champion, raced to a 5-0 lead with Stephens winning a total of just eight points.
But the American, no stranger to the Paris big stage after reaching the final in 2018, was not done yet, clawing her way back and saving a set point at 5-2 to cut the deficit.
With her own first serve wilting, Sabalenka, in complete free fall by now, missed another two set points at 5-4 on Stephens' serve before her opponent leveled and then held to take it to a tiebreak.
Sabalenka, looking to add a second Grand Slam to her maiden triumph, managed to pull herself together at the last moment, clinching the first set on her fourth opportunity.
"I think it was just like [a] few key moments which I didn't finish right, and then she start[ed] to believe in herself a little bit more," Sabalenka said. "People start[ed] to support her more. She kind of play[ed] with that crush and was like going for the shots. I think she played unbelievable tennis.
"I felt like I kind of like dropped my level for a little bit -- not for a little bit, actually, for five games. But, yeah, I'm super happy that I was able to win the first set."
She cut down on the unforced errors in the second set but again Stephens battled back from 4-2 down to level before Sabalenka broke again to go 5-4 up and serve out the match.
"It's good preparation. If you can get through this match, you can get through whatever happens to you. It was [a] really tough, tough match," Sabalenka said.
In the quarterfinals, Sabalenka will face Elina Svitolina, who defeated No. 9 Daria Kasatkina 6-4, 7-6 (5). Svitolina, who is from Ukraine, skipped the postmatch handshake against her Russian opponent because of the ongoing war; Kasatkina offered a thumbs-up to Svitolina.
Just like after her third-round victory, Sabalenka did not attend the traditional postmatch news conference. Instead, the tournament allowed her to speak with a member of the WTA's editorial staff.
At media sessions following each of her first two matches in Paris, Sabalenka was asked about her stance on the war in Ukraine, which began in February 2022, when Russia invaded that country with help from Belarus.
Pavlyuchenkova, who missed last year's tournament as part of a lengthy absence with a knee injury, got past a third consecutive seeded opponent, No. 28 Elise Mertens, by a 3-6, 7-6 (3), 6-3 score.
Muchova was a 6-4, 6-4 winner against Elina Avanesyan, who lost in qualifying but got into the main draw when another player withdrew.
Reuters and The Associated Press contributed to this report.