Robert Deutsch-USA TODAY Sports

Alexandre Muller and Sebastian Baez recorded big upsets Monday to advance to the fourth round of the Internazionali BNL d'Italia in Rome.

Muller, a Frenchman, notched a 3-6, 6-3, 6-2 win over fourth-seeded Andrey Rublev of Russia. Rublev won the Madrid Open in his last tournament.

Baez, the No. 17 seed from Argentina, also rallied from an early deficit to post a 2-6, 6-2, 6-3 win over No. 10 Holger Rune of Denmark.

Muller had six aces without a double fault while Rublev had five aces against four double faults. Muller had just six unforced errors while advancing to face No. 21 seed Nicolas Jarry of Chile.

Jarry had a 37-10 edge in winners, including eight aces, while registering a 6-2, 4-6, 6-4 victory over Italy's Stefano Napolitano.

Meanwhile, Baez converted 5 of 6 break points and had just 10 unforced errors in his victory. Rune had 24 winners but also had 21 unforced errors.

Baez will next face No. 7 seed Hubert Hurkacz of Poland. Hurkacz had an 11-2 edge in aces while compiling a 7-6 (7), 6-2 victory over No. 25 seed Tomas Martin Etcheverry of Argentina.

Hurkacz said he now has more confidence on clay courts than he did in the past.

"I think so. Definitely, especially matches like this with Tomas, who's such a good player and a good competitor," Hurkacz said. "It gives confidence that I was able to get through this one."

Second-seed Daniil Medvedev of Russia was pushed hard before notching a 7-6 (5), 2-6, 7-5 win over Hamad Medjedovic of Serbia.

Medvedev, the reigning champion in Rome, overcame 10 double faults and committed just 24 unforced errors to 44 for Medjedovic.

"I felt like I started the match well and then in a way it was only going downhill," Medvedev said. "My serve was not there, my shots were not aggressive enough when I needed to. Because many times I would like to play the rhythm I played, but I would also like from time to time to surprise my opponent with some good shots. Today I was not able to do it.

"At one moment in the match, I thought what I was doing would not be enough to win the match."

Medvedev will next face No. 14 seed Tommy Paul, who recorded a 6-4, 6-3 victory over Germany's Dominik Koepfer.

No. 6 seed Stefanos Tsitsipas of Greece advanced with a 6-2, 7-6 (1) triumph over British No. 27 seed Cameron Norrie.

Tsitsipas next faces No. 9 Alex de Minaur after the Australian was a 6-7 (2), 6-4, 6-4 winner over Canadian No. 18 Felix Auger-Aliassime.

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