Far more seats were empty than occupied when the second-round match between No. 1 seed Karolina Pliskova and 127th-ranked Nicole Gibbs commenced in Arthur Ashe Stadium.
"In the second set I started to serve better and get easy points with my first serve, which was much needed", said Pliskova.
Pliskova, who went to the top of the rankings after Wimbledon, was outplayed for much of the first set.
Fourth-seeded Elina Svitolina also advanced with a 6-4, 6-4 victory over Evgeniya Rodina, who had routed Eugenie Bouchard in the first round.
American Shelby Rogers and Australian Daria Gavrilova set a record of 3hr 33min for the longest women's singles match played at the US Open on Thursday.
Zhang's tactic of going up to the net more often managed to work well as she held serve in the nervy game for a 4-1 lead.
Thiem eased into the fourth round with a 7-5, 6-3, 6-4 victory over No. 30 Adrian Mannarino of France.
"It's not only about the points, but I just felt I really can play well here", said Pliskova, who will next face American Jennifer Brady.
The Czech world No 1, who reached the final in NY past year, required three sets to defeat American home favourite Nicole Gibbs in the second round and was on the brink of defeat before rallying to record a hard fought 3-6 7-5 6-4 success. "Yeah, I'm just going to go out there and have some fun".
Williams will play Suarez Navarro in the fourth round for her chance to reach the US Open quarterfinals for the 12 time.
Federer won five consecutive U.S. Open championships from 2004-08 and also was the runner-up twice, including two years ago.
Meanwhile, Lucie Safarova, the women's world No 1 doubles player, was another Czech player to progress to the last 16 with a comfortable 6-3 6-2 victory over Japan's Kurumi Nara and will next meet CoCo Vandeweghe. However, the Czech hit her best forehand of the day, which was just her third forehand victor in the set, to save a match point before breaking back to level the scores and keep herself in contention for the comeback victory. "I'm just happy that I have another match in my pocket and I'll just try to improve in the next one".
Also advancing were No. 33 seed Philipp Kohlschreiber, a straight-sets victor over Australian John Millman, and Alexandr Dolgopolov, who routed Viktor Troicki 6-1, 6-0, 6-4.
"It's quite normal to have this, and I would prefer to have on the top and have these kind of expectations than be somewhere out of top 20 or something and - to don't have that", Svitolina said.