Rome: World number two Rafael Nadal will begin his quest for record-breaking eighth Rome Masters title, when he squares off with Bosnian tennis star Damir Dzumhur in their round-of-32 clash in Italy on Wednesday.
Defending champion Alexander Zverev beat Italian wild-card entry Matteo Berrettini 7-5, 6-2.
"I played very well today", said Thiem, who beat Rafael Nadal in the Madrid Open semifinals last week. He will now take on British number one Kyle Edmund, who saved the only break point he faced in a 6-2 7-6 (3) victory over France's Lucas Pouille. The 16-time Grand Slam victor next takes on either Canadian Denis Shapovalov, 19, or Robin Haase of the Netherlands.
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.
In the decider, a single break of serve in the seventh game gave Fognini the opportunity and he held to his two serves to win 6/3.Kei Nishikori denied Grigor Dimitrov a 27th birthday win to reach the Internazionali BNL d'Italia third round on Wednesday, defeating the World No. 4 6-7 (4), 7-5, 6-4.
In the women's tournament, top seeds Simona Halep and Caroline Wozniacki advanced to the third round in straight sets.
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The Association of British Bookmakers (ABB) warned the move will be a "hammer blow" to High Street bookmakers and threaten thousands of jobs.
As a result, the 31-year-old lost his top rank to long-time rival Roger Federer in the updated ATP Rankings, but Nadal can retain his top spot with a win at the Rome Masters.
Halep next plays 13th-seeded American Madison Keys, who battled past Croatian Donna Vekic 7-6 (7/2), 7-6 (7/0), for a place in the last eight.
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 just really wanted to win this match against a really classy player", said the five-time Grand Slam champion. "But I think this is the first match of the year that I've felt like this", insisted Osaka, who struggled with her backhand.
World No 5 Karolina Pliskova was eliminated by Maria Sakkari in controversial circumstances, prompting the Czech to react by smashing her racket against the umpire's chair at the end of the match.