Sixth seed Thiem crashed out just a week after inflicting a first clay-court defeat on Nadal in over a year in Madrid which cost the Spaniard the world number one ranking.
Rafael Nadal got his clay season back on track with a 6-1 6-0 second-round demolition of Damir Dzumhur at the Internazionali d'Italia.
It is the 13th time in his career Nadal has dropped only one game in a match, but he is still looking for his first "double bagel".
"After a loss in Madrid, it's important to come back strong".
"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.
Earlier, Fabio Fognini got the Italian Open crowd fired up with a 6-4, 1-6, 6-3 win over sixth-seeded Thiem.
Novak Djokovic, a four-time victor in Rome, powered into the third round with a convincing 6-4 6-2 win over Georgian Nikoloz Basilashvili. "It's a loss which is not too painful, which is just motivating me for the next weeks", the Austrian said.
Djokovic will next face Albert Ramos-Vinolas, who rallied past eighth-seeded John Isner 6-7 (5), 7-6 (2), 7-6 (5).
"It was a good match, actually, from both of us, I would say", said Thiem. So I'm disappointed that I lost, obviously.
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.
After the match, Pliskova didn't shake hands with the chair umpire and struck the chair several times with her racket.
The controversial shot came in the third set with the Czech serving at 5-5 (30/30). The chair umpire acknowledged that she "lost" the ball mark and therefore said the point should be awarded to Sakkari.
Earlier, top women's seed Simona Halep needed just under an hour to advance 6-1, 6-0 past Naomi Osaka to avenge her defeat to the Japanese player in Indian Wells. She could not hide her fury as she went on to lose the match 3-6, 6-3, 7-5.
"It was one of those helpless feelings", conceded 20-year-old Osaka who could be heard saying "I want to cry" courtside.
"I like to slide on the clay and today was easy for me".
Halep reached the final in Rome past year and needs to reach the quarter-finals this time to retain her world number one ranking.
Former No. 1 Angelique Kerber rallied past Irina-Camelia Begu 3-6, 7-5, 7-5, and 14th-seeded Daria Kasatkina eliminated American qualifier Danielle Collins 6-2, 6-3.