Gauff will play fellow countrywoman Sloane Stephens in a major for the second time in a year.
The reigning Madrid Open champion went a set down in the match but came back from what seemed like a dire situation to move on to the semis.
Sabalenka defeated American Anisimova for the first time in five tries. Garin was clueless to Zverev’s ball-striking.
Seventh seed Danielle Collins was in high spirits after defeating former world no. 1 Simona Halep but her joy was cut short by the unseeded Amanda Anisimova.
Amanda Anisimova will next face Ashleigh Barty after ending Naomi Osaka's title defence in the third round of the Australian Open.
The Czech star fired 24 aces and saved a match point on her way to beat Bianca Andreescu in a thrilling three-set encounter.
Gauff downs Anisimova in straight sets to enter the semifinals of the Emilia-Romagna Open and will next play Katerina Siniakova.