Djokovic took a long bathroom break after the second set, much to Sousa’s annoyance, and then went off court again early in the third set after calling for the doctor.

However, the sixth seed did not face too many hairy moments in a 6-3 6-4 6-3 win that took exactly two hours.

Djokovic said: “I’m very happy to get this one done in straight sets. It was much more difficult than the score indicated. Credit to Joao for fighting, he brought a lot of intensity on the court.

It was very tough conditions, especially the first hour-and-a-half. We are putting in all the work but sometimes you just have to survive.

The extreme heat policy was again in action, with temperatures climbing over 30C and significant humidity, meaning a 10-minute break between the third and fourth sets, although this match did not get that far.

After a relatively comfortable first set, Djokovic found himself in trouble at the start of the second as Sousa, the first Portuguese player ever to reach the fourth round of a grand slam, broke for a 2-1 lead.

The 13-time grand slam champion hit straight back and went on to take the set but was clearly not enjoying himself in the heat, although his struggles were not as severe as during his first-round clash with Marton Fucsovics.

Djokovic will face the winner of last night’s clash between Roger Federer and John Millman, while also through to the last eight is Japan’s Kei Nishikori.

The 21st seed beat Philipp Kohlschreiber 6-3 6-2 7-5 and could next face a rematch of the 2014 final, which he lost to Marin Cilic. Nishikori missed this tournament last year and the Australian Open in January because of a wrist injury and dropped down to the second-tier Challenger Tour to begin his path back.

He said: “I was playing one match at a time, because I didn’t have any confidence and I was still worried about my wrist.

“The clay-court season was great then first time going to the quarter-finals in Wimbledon. It’s going well this year.”

John Isner continued his career-best season by defeating Milos Raonic in five sets to reach the quarter-finals of the US Open for the first time in seven years.

Having reached his first grand slam semi-final at Wimbledon — before losing the epic encounter against Kevin Anderson — Isner has maintained his momentum.

The biggest surprise of yesterday’s clash between the two big servers was that it did not feature a single tie-break, with 11th seed Isner winning 3-6 6-3 6-4 3-6 6-2.

Defending women’s champion Sloane Stephens eased into the last eight with a 6-3 6-3 victory over 15th seed Elise Mertens.

Stephens is the only top-five seed remaining and has been increasingly impressive as she bids to win a second grand slam title.