No 2 seed takes on Ons Jabeur of Tunisia in the next round
The Belarusian booked her first Grand Slam quarter-final with a battling 6-3 4-6 6-3 victory on Court Three.
Sabalenka looked well in control when she took the first set, but 18th seed Rybakina crashed down six aces and made just four unforced errors to Sabalenka’s 15 to level the match.
But after a nip-and-tuck seven games in the decider, Sabalenka pulled away.
She won the last eight points of the match, forcing the crucial break for 5-3 and serving out to love.
The 23-year-old will face Tunisia’s Ons Jabeur on Tuesday.
Jabeur, seeded 21st in the women’s singles draw, beat last year’s French Open champion Iga Swiatek in three sets on Monday.
The Tunisian came from behind to emerge a 5-7 6-1 6-1 victor on Court Two.