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World number two Alcaraz was playing China’s Wu, who belied his ranking of 560.
Both players produced blistering groundstrokes in a high-quality first set which Wu started strongly.
He had the support of the home crowd and hit some eye-catching shots, especially off his backhand.
However, his serve came under the greater pressure, and while he managed to get to a tie-break he lost it to go a set down.
In the second set, Wu thought he had saved a break point in the sixth game only for his first serve to be deemed out after an Alcaraz review.
The Spaniard then won the point to register the first break of the match and go 4-2 up, before going on to serve out the match.
“He’s recovering his level. He’s coming back from injury so his level deserves to be at the top for sure,” said Alcaraz.
“If he is still playing at this level and keeps going then I’m going to see him around more often.
“I’m really happy to get through. I’m not used to the way I felt on court. He’s a really powerful player and played strong. I felt like I was not dominating the game.”
Daniil Medvedev also made it through, battling to a 5-7 6-4 6-4 victory against Matteo Arnaldi in two hours 44 minutes.
Medvedev achieved the decisive break in the ninth game of the deciding set before going on to serve out for the match and will play either Stefanos Tsitsipas or Alexandre Muller in the last 16.
“It was a very tough match, a very close one,” said Medvedev. “I actually felt like that’s where tennis is funny. I felt like in the first set, I was probably the better player, had more opportunities. I didn’t manage to [win] it, played a bad game at the end of the set.
“In the other sets, I thought it was closer, maybe even he had the edge on some of the moments. But, that’s why tennis is crazy, you can win when you don’t expect it, and lose when you expect to win, so I’m happy to be here again in two days.”
Play was cancelled on the outside courts for the second day running because of the rain, with matches only possible under the roof of the main stadium show court.
