After a surprise summer loss a year ago to Denis Shapovalov, Rafael Nadal gained revenge on his surface, slamming the Canadian 6-4, 6-1 to reach the Rome Masters quarterfinals. His only ATP-level experience on clay prior to this season was a first-round qualifying loss at the French Open.
After dropping a tightly contested second set, Shapovalov took control in the third.
Nadal finally got the break and Shapovalov did not get a point against serve until game eight - he only had two when the world number two closed out the first set by forcing the Canadian deep and wide before rushing to the net to close the angles.
"I played very well today", said Thiem.
Djokovic, a four-time victor, is on the comeback trail three months after elbow surgery and eased past Georgia's Nikoloz Basilashvili 6-4, 6-2.
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.
The Serb will next play Spaniard Albert Ramos Vinolas who squeezed past American eighth seed John Isner 6-7 (5/7), 7-6 (7/2), 7-6 (7/5).
Defending champion Alexander Zverev needed eight match points before completing a 7-5, 7-6 (11) win over Kyle Edmund.
But the 37-year-old had to save a match point before seeing off Russian Elena Vesnina 6-2, 4-6, 7-5 and will next face Anett Kontaveit. "I will do all of the exams now and then I will try to make a good decision for the future".
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"We're finally connecting and I think that's the most attractive thing", Fognini said of the crowd, which whistled him off the court following an erratic performance a few years ago.
"I beat a top clay-courter", Fognini added. "And I think it was harder than what the score showed".
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.
"It's a loss which is not too painful, which is just motivating me for the next weeks", the Austrian said.
In women's action, Simona Halep routed Naomi Osaka 6-1, 6-0 for the first of two wins she needs this week to hold on to the No. 1 ranking.
Halep plays US Open champion Sloane Stephens or seventh-seeded Caroline Garcia.
Cilic will play 10th-seeded Pablo Carreno Busta, who beat Aljaz Bedene 6-4, 6-7, 6-2.
Meanwhile, former world number one Karolina Pliskova smashed the umpire's chair in frustration after she lost to Greece's Maria Sakkari in the second round.