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Alcaraz made to ‘suffer’ in four-set win at Roland Garros
The second seed had looked to be making light work of his opponent with a two-set lead, before a revival from the Bosnian pushed their encounter into a fourth set under the lights on Court Philippe Chatrier.
Spaniard Alcaraz, seeking to become the first man since compatriot Rafael Nadal in 2020 to retain the Roland Garros title, eventually ground out a 6-1 6-3 4-6 6-4 success.
"I didn't enjoy it too much," said the 22-year-old. "I suffered quite a lot but I'm happy to have played a good match with Damir.
"That's why it's difficult to win Grand Slams because you have to maintain your focus over three or four hours.
"The first two sets were under control and then he decided to play deeper and more aggressive. My energy went down and it was hard to push, but I had to give everything I had inside. I'm proud to get the win in the end."
Alcaraz will face 13th seed Ben Shelton next after the American beat Italy's Matteo Gigante 6-3 6-3 6-4 earlier on Friday.