Sabalenka powers into Roland Garros quarter-finals
The Belarusian battled through a tight opening set against the American 16th seed and then needed eight match points to clinch a 7-5, 6-3 victory on Court Suzanne Lenglen.
Sabalenka, who was the pre-tournament favourite, will face Olympic champion Zheng Qinwen in the last eight after the Chinese star edged past Liudmila Samsonova.
Zheng beat Sabalenka for the first time in their seven meetings in the Italian Open quarter-finals in the build-up to Roland Garros.
Anisimova holds a 5-3 winning record over Sabalenka but has now lost their last two matches.
The 23-year-old, a French Open semi-finalist in 2019, won her maiden WTA 1000 title in Doha earlier this season.
She pushed Sabalenka in the first set, breaking the top seed when she was serving to clinch the opener.
But two missed break points in the 11th game proved costly as Sabalenka went on to secure a one-set lead.
The three-time Grand Slam champion quickly built a 3-0 advantage in the second set.
Anisimova showed real grit to save six match points in a marathon hold of serve to cut the deficit to 5-3, but Sabalenka finally finished it off on her own serve at the eighth time of asking with a thumping backhand winner.