Zverev, 23, was in top form in the first set as he displayed an impressive serve and volley game to triumph 6-2 in just 30 minutes.
Williams had to come back from a set and a break down to storm to a 4-6, 6-3, 6-2 win against Bulgaria's Tsvetana Pironkova while Azarenka dropped just one game against 16th seed Elise Mertens of Belgium to seal a spot in the semifinals.
"My waist disc herniation has been acting up again," she said, adding that she would be back next year.
The relatively unheralded Veszelka, meanwhile, leaped to 16.69m in the third round and bowed out with a 16.66m jump to land the upset victory at the World Athletics Continental Tour Silver meeting.
The competition starts at Shimei Bay and passes through the scenic Jiajing Island, which is about 1.5 nautical miles (about three kilometers) from the coast of Shimei Bay. The competitors return to Shimei Bay Beach after making a circle around Jiajing Island.
Perhaps mindful of its drivers' tyre troubles at Silverstone earlier in the season, Mercedes engineers ordered Hamilton and Bottas to stay off the Mugello circuit's kerbs - though even after doing so, both drivers appeared to have enough pace to keep the chasing pack at bay.
Other players such as Piccini and Florenzi have also moved on and with no new faces other than returning loanees, new coach Javi Garcia much be wondering what he has got himself into.
"I consider New York my second home, I really love the atmosphere, even though sadly there are no people here, I really feel this court really suits me well," Osaka said.
"We beat ourselves today. Our performance is hard to explain but it is a bitter defeat, that is for sure," Hertha Berlin head coach Bruno Labbadia said.
"There wasn't a gap and if you use your elbows to open it up, I think it's completely against the rules," Van Aert said.
Frankfurt were more clinical with their chances and punished courageous Nuremberg as Bas Dost's volley assist allowed Andre Silva to nod home the opener six minutes into the second half.