Novak Djokovic overcame humid conditions and testing opposition in Joao Sousa to set up a potential US Open quarter-final against Roger Federer.
The two-time champion showed signs of physical discomfort but, despite receiving medical attention during the third set, he progressed with a 6-3 6-4 6-3 victory against his unseeded Portuguese opponent on Arthur Ashe Stadium.
Djokovic, who also struggled with the heat in his first-round victory against Marton Fucsovics, was not at his best but will now face Federer if the world No 2 defeats John Millman in Monday's night match.
"Very happy to get this one done in straight sets," Djokovic said
"It was much more difficult than the score indicated. He brought a lot of intensity on the court. It was tough conditions, especially in the first hour on court, really humid."
The 31-year-old broke twice on his way to securing the first set in assured fashion as Sousa struggled to contend with the former world No 1's consistency from the back of the court.
Sousa, who in reaching the fourth round was enjoying his best run at a Grand Slam, proved a feisty competitor and despite his lack of power offered himself encouragement with his first break of the match after a series of unforced errors from Djokovic.
But a frustrated Djokovic responded immediately to get back on serve and after breaking for a second time in decisive fashion went off court for a bathroom break.
Leading 2-1 in the third set, Djokovic received a medical timeout off court but, despite Sousa's best efforts to extend the match into a fourth set, he raised his game to break in the eighth game before serving out for victory.
"I prefer not talking about how difficult it is," he added when asked about the conditions.
"We are blessed to play the sport we love. Just trying to cherish the moment of the court. I'm not 21 anymore, I still don't feel old but at same time there is a little biological clock that's not in your favour."
Kei Nishikori also booked his place in the quarter-finals as the 2014 finalist proved too stern a test for Philipp Kohlschreiber.
The Japanese 21st seed hit 29 winners to end the run of the experienced German, who knocked out world No 4 Alexander Zverev in the third round, 6-3 6-2 7-5.
Nishikori will face Marin Cilic, who beat him in the New York showpiece four years ago, after the Croatian world No 7 defeated David Goffin 7-6 (8-6) 6-2 6-4.
We have every major tennis event covered from all angles via our website skysports.com/tennis. On the move? Head to our app for mobile devices and iPad, or follow our Twitter account @SkySportsTennis to join in the conversation.
Tennis is back on Sky Sports screens with the Laver Cup in September while we will also have coverage of the ATP Finals in November with every match live on Sky Sports. But first, we will be across the final major of the year in New York as the US Open right through to the final with live blogs, reports, features and reaction.