Having reached the final in Madrid where she lost to world No 1 Iga Swiatek, Sabalenka has now won seven of her last 8 matches on clay.
This was also her 90th career win at a WTA 1000 event, joint most wins in this category since 2018 along with Swiatek.
Sabalenka, ranked No 2, will play the winner of the match between Ukrainian Elina Svitolina, the No 16 seed, and Russian Anna Kalinskaya, the No 23 seed, next.
Ahead of her victory, the Belarusian won against American qualifier Katie Volynets (4-6, 6-3, 6-2).
Yastremska, ranked No 33, won against German qualifier Laura Siegemund (4-6, 7-5, 6-2) in the previous round of the Rome tournament.
Rome WTA 1000, other round of 32 results (Foro Italico, clay, USD 5,509,771):
- Irina-Camelia Begu beat Elise Mertens (27): 6-2, 6-0
- Maria Sakkari (5) beat Anhelina Kalinina (30): 7-6 (4), 6-0
- Coco Gauff (3) beat Jaqueline Cristian (LL): 6-1, 0-6, 6-3
- Sorana Cirstea (28) beat Marketa Vondrousova (6): 7-6 (1), 6-3
- Madison Keys (18) beat Beatriz Haddad Maia (12): 6-4, 4-6, 6-3
- Qinwen Zheng (7) beat Linda Noskova (29): 3-6, 6-1, 6-2
- Naomi Osaka beat Daria Kasatkina (10): 6-3, 6-3
- Angelique Kerber beat Aliaksandra Sasnovich (Q): 6-3, 7-6 (4)
- Paula Badosa beat Diana Shnaider: 5-7, 6-4, 6-4
- Iga Swiatek (1) beat Yulia Putintseva: 6-3, 6-4
- Elina Svitolina vs. Anna Kalinskaya
- Danielle Collins vs. Caroline Garcia
- Victoria Azarenka vs. Mayar Sherif
- Sara Sorribes Tormo vs. Jelena Ostapenko
- Sofia Kenin vs. Rebecca Sramkova
