Seven-time champion Rafael Nadal has methodically worn down Denis Shapovalov in a 6-4 6-1 win to reach the Italian Open quarter-finals and gain a measure of revenge against the Canadian. Meanwhile, Djokovic moved into his first quarter-final since Wimbledon last July when he defeated Spain's Albert Ramos-Vinolas 6-1, 7-5.
The Spaniard, who received a first-round bye, kicked off his campaign in Foro Italico with a comfortable 6-1, 6-0 win over Bosnian tennis star Damir Dzumhur in their round-of-32 clash that lasted exactly one hour.
"I just really wanted to win this match against a really classy player", said the five-time Grand Slam champion. "So, I think it's a good thing that I played here".
Nadal leveled at two-all and later got the crucial break to lead 4-3.
The Spaniard will next take on Fognini, a player he holds a 10-3 record against including five straight wins in their most recent matches.
"He was really serving big and I had some mistakes with the return", Nadal said.
Thiem says it will not be an issue playing one week before the start of the French Open and will spend the time making a few tweaks while trying to build some momentum at the same time.
But the Austrian says he is optimistic about putting together a good run at Roland Garros, which starts on May 27, and where Thiem has reached the semi-finals in the past two years.
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Nishikori, who like Djokovic is trying to come back from injury, was in complete control against Philipp Kohlschreiber, defeating the German 6-1 6-2.
Elsewhere, fifth seed Juan Martin Del Potro retired hurt while 6-4, 5-4 down against ninth seed David Goffin, while Marin Cilic eased past Benoit Paire 6-4, 6-4.
Number one seed Simona Halep of Romania made it through to the quarter-finals before a ball was struck as her opponent, Madison Keys of the United States, had to retire hurt before she took to the court.
Halep needed to reach the quarterfinals and progress further than No. 2 Caroline Wozniacki to hold onto the top spot, and she accomplished the first task.
Halep will next play either U.S. Open champion Sloane Stephens or seventh-seeded Caroline Garcia.
Four-time champion Novak Djokovic also advanced, beating Georgian qualifier Nikoloz Basilashvili 6-4, 6-2. Due to that, the southpaw not only failed to defend his Madrid title but also had to relinquish the top ranking to his greatest nemesis, Roger Federer.
The biggest upset of the day belonged to Japan's Kei Nishikori, who came from behind to upend third-seeded Bulgarian Grigor Dimitrov 6-7 (4), 7-5, 6-4.