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. But the sixth seed did not face too many hairy moments in a 6-3 6-4 6-3 victory 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.”
Also through to the last eight is Japan’s Kei Nishikori.
In the women’s draw, Naomi Osaka reached her first grand slam quarter-final with victory over fellow 20-year-old Aryna Sabalenka.
In one of the most highly-anticipated women’s matches of the tournament, between two players who are expected to face each other many more times on the big stage, it was Japanese-American Osaka who prevailed 6-3 2-6 6-4.
Last year’s runner-up Madison Keys is the highest seed left in the bottom half of the draw at 14 and she breezed through to the last eight again with a 6-1 6-3 victory over Dominika Cibulkova.
Jamie Murray and Bruno Soares continued their fine form with victory over Robin Haase and Matwe Middlekoop to go through to the men’s doubles quarter-finals.
Murray and Soares are yet to drop a set in three matches and survived some sticky moments in the first set to win 7-6 (7/4) 6-4.
The fourth seeds, who won their first Masters title together in Cincinnati just before the tournament, claimed their second grand slam title here two years ago but have not made it past the last eight at any of the slams since.
Murray said: “We’re playing well. We came through some difficult moments today.
“We went down 0-40 on Bruno’s serve and we won some really long points to get through that game and then we played really well in the tie-break.
“The second set we were on top the whole way through, had chances to get the second break, didn’t quite do it but we did a good job.”