Novak Djokovic defied a shoulder injury to defeat American Kudla in straight sets on Friday night.
The Serbian star was superb in dispatching the home player on the Arthur Ashe court.
Despite going into the match with a shoulder injury, Djokovic looked flawless at times with his energetic play and strong serving.
Now, he will have a rematch of the 2016 final, as he prepares to take on Swiss star Stan Wawrinka.
Wawrinka defeated Paolo Lornezi in straight sets in the second in a back-to-back set of matches.
And Djokovic is wary of the challenge Wawrinka possesses, and told ESPN that he will have to be at his best to get through the fourth round.
“We had some great battles over the years everywhere, but particularly here,” he said.
“I lost to him the last time we played on this court, in the final in 2016.
“He’s a three-time grand slam champion, someone that possesses a game with a lot of power and quality.
“He’s a great guy, we practice together a lot, so may the best man win.”
The 32-year-old defending champion was close to withdrawing from the match due to his shoulder injury, after skipping practice twice.
But he insisted that he was not in pain during the match.
“That I managed to play almost pain-free,” he replied when asked what the main highlight of the match was for him.
“That’s a big improvement from the last match.
“I didn’t know how the body would react and I’m just glad to finish the match injury-free.
“Look, I’m not going to go into the medical details but it was definitely bothering me over the last couple of weeks, especially in the last match, so I didn’t practice yesterday, I just wanted to give myself the time and do everything possible to be here tonight.
“I want to thank everyone for staying this late and supporting both of us players.”