In women's action, Simona Halep routed Naomi Osaka 6-1, 6-0 for the first of two wins she needs this week to keep Caroline Wozniacki from taking her No. 1 ranking.
"It was important, after a loss in Madrid, to come back strong, and that's what I did today", said Nadal following his demolition of Dzumhur. His victory against Thiem was like a revenge match as it reduced the gap in the number of victories between the two players (4 wins for the Austrian player against 2 for the German player).
However, before they can look ahead to a blockbuster encounter, Nadal will first have to get past Dutchman Robin Haase/Canadian Denis Shapovalov, while Djokovic next faces Spain's Albert Ramos-Vinolas, who defeated American John Isner yesterday.
Djokovic, a four-time victor of the Italian Open, also had little trouble in his second round match, defeating Georgia's Nikoloz Basilashvili 6-4, 6-2 in one hour and 18 minutes.
"We're finally connecting and I think that's the most lovely thing", Fognini said of the crowd, which whistled him off the court following an erratic performance a few years ago.
The second seed eased past Berrettini 7-5, 6-2 to join former winners Rafael Nadal and Novak Djokovic in the third round at the Foro Italico as Austrian Dominic Thiem fell at the first hurdle.
In the most high-profile match on Day 4, Japan's Kei Nishikori battled past world No 4 Grigor Dimitrov 6-7, 7-5, 6-4. "I ruined a few flowers but I think the federation can afford to buy some new ones".
"I beat a top clay-courter", Fognini added.
Fognini went onto see out the match to advance to the last 16, whilst Thiem will prepare for the Lyon Open in France next week, in preparation for a tilt at the prestigious French Open in Paris at the end of the month.
"I went on court with the right intensity".
"She knew it and we were having a lot of backhand rallies, other than that I couldn't say what happened."I feel like I've played her the most of any player, this was the third time this year". Last year, I did really well. In the middle of the sixth game the Chair Umpire over-ruled a call after inspecting the point where the ball landed.
Nishikori dropped the first set but mounted an impressive comeback to secure a hard-fought 6-7, (4-7), 7-5, 6-4 victory. He broke in the 11th game and later served out the set.