However, women's singles star Simona Halep's disappointing run at the Flushing Meadows continued.
Here are the details.
Rafa through without striking a ball
Three-time US Open champion Rafael Nadal got a walkover in his second round match at the year's final Grand Slam. Rafa advanced without striking a ball when injury-plagued Thanasi Kokkinakis pulled out with a right shoulder problem.
Zverev wins a thriller, Medvedev battles past cramp
Meanwhile, German Zverev, the sixth seed, survived a second successive five-set marathon by outlasting American Frances Tiafoe 6-3, 3-6, 6-2, 2-6, 6-3 to advance.
The promising fifth seed Daniil Medvedev was struck down by cramp during a 6-3, 7-5, 5-7, 6-3 win over Bolivia's Hugo Dellien.
"I'm not sure what happened today and why I started cramping suddenly," Medvedev said.
Wawrinka and Kyrgios win respective matches
2016 US Open champion Stan Wawrinka beat Jeremy Chardy in four sets and is on a fourth-round collision course with world number one Novak Djokovic. Meanwhile, Australian 28th seed Nick Kyrgios rolled past 104th-ranked French wildcard Antoine Hoang 6-4, 6-2, 6-4.
Halep's poor run of form continues
Halep crashed out early for a third year running.
The Romanian blew a match point in a tense three-set loss to 116th-ranked Taylor Townsend.
Townsend survived a thriller to beat Halep 2-6, 6-3, 7-6 (7/4).
"I was not inspired at all today, but I fought. I thought when I came back that I will take it and I will win it," Halep said.
Gauff sets up Naomi Osaka showdown
Fifteen-year-old American sensation Coco Gauff has set up a cracking showdown with defending champion Naomi Osaka.
Coco beat Hungarian qualifier Timea Babos 6-2, 4-6, 6-4 to become the youngest player in the last 32 at a US Open since Anna Kournikova in 1996.
"It has been amazing. I'm just so happy to get through," Gauff said.
Osaka gets it right, Kvitova knocked out
Top seed Osaka tamed 53rd-ranked Magda Linette of Poland, sweeping to a 6-2, 6-4 victory. "I feel like I had my moments where I played really well," Osaka said. Meanwhile, Andrea Petkovic knocked out Czech sixth seed Petra Kvitova 6-4, 6-4.