The second seed Spaniard won 6-4 6-4 4-6 6-3 in his second round match against Lithuania's Ricardas Berankis.
The World No 1 defeated Dutch player Lesley Pattinama Kerkhove 6-4, 4-6, 6-3.
The fourth seed, Tsitsipas, won 6-2 6-3 7-5 on Court One on Thursday.
The golden girl of Britain suffered a 6-3, 6-3 loss in the second round.
The top seed crushed the Australian 6-1 6-4 6-2 in their second round meeting.
French debutant Harmony Tan, ranked 115th, threw a spanner into Williams' eagerly anticipated return with a nerve-shredding 7-5 1-6 7-6(7) win.
The Spaniard beat Francisco Cerundolo 6-4 6-3 3-6 6-4 in the first round.
Sweden's Elias Ymer replaced Berrettini in the men's draw.
He secured victory with an ace on his first match point and will next meet either Thanasi Kokkinakis of Australia or Poland's Kamil Majchrzak.
Hurkacz, whose power is suited to grass courts, is third on the list of number of aces hit on the ATP Tour this year with 452 -- behind big-serving Americans John Isner and Reilly Opelka.