Sramkova, ranked No 120 in the world, will face the winner of the match between Spaniard Sara Sorribes Tormo and Latvian Jelena Ostapenko, the No 9 seed, next.
The Slovak’s run this week will ensure she makes her top 1000 debut in the updated world rankings after Rome, with her previous career high being No 111.
In the previous rounds of the tournament, the Slovak beat Italian wildcard Giorgia Pedone (6-4, 6-1) and No 26 seed Katie Boulter (6-4, 7-6 (8)).
Kenin, ranked No 58, won against Italian Lucia Bronzetti (6-3, 6-2) and edged out Tunisian Ons Jabeur, the No 8 seed (7-5, 2-6, 6-4) earlier in the week.
Rome WTA 1000, other round of 32 results (Foro Italico, clay, USD 5,509,771):
- Aryna Sabalenka (2) beat Dayana Yastremska (32): 6-4, 6-2
- 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
