Nadal, who lost his number world one ranking after his 14-match winning run on clay was snapped by Thiem in the Madrid Open quarter-finals last week, was back to his best as he wrapped up victory with a blistering forehand victor.
Rounding out the day's action, 10th-seeded Spaniard Pablo Carreno Busta bested American Steve Johnson 6-4, 2-6, 6-4; Frenchman Benoit Paire upset 14th-seeded Argentine Diego Schwartzman 2-6, 6-4, 6-2 and Great Britain's Kyle Edmund defeated 16th-seeded Frenchman Lucas Pouille 6-2, 7-6 (3).
Rafael Nadal has put his loss to Dominic Thiem in Madrid behind him by dropping just one game against Damir Dzumhur in his opening match of the Italian Open. "And that's what I did today", said Nadal, who is targeting an eighth Rome title and first since 2013.
The 31-year-old, who claimed the 11th titles of his career at both Monte-Carlo and Barcelona, took the first set in 34 minutes coasting to victory in just one hour.
The former world number one, whose 21-match unbeaten run on clay ended last week, had a first-round bye and will play Denis Shapovalov or Robin Haase next.
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.
Third seed Grigor Dimitrov did not have a birthday to remember as he fell 7-6 (4), 5-7, 4-6 to Kei Nishikori.
The Serbia will next play Spaniard Albert Ramos Vinolas who needed three sets to get past American eighth seed John Isner 6-7 (5/7), 7-6 (7/2), 7-6 (7/5).
Turkish Banker Sentenced To 32 Months In Iran Sanctions Case
The wealthy Zarrab, arrested a year before Atilla, initially attracted considerable attention to the case. Earlier in 2018, Atilla was convicted of taking part in a scheme to help Iran evade US sanctions.
Osaka had every reason to be confident heading into her clash with Halep after beating her 6-3, 6-0 at Indian Wells in March, but on this occasion, she collapsed after a wasteful start.
Wozniacki can reclaim the world number one ranking from Halep, last year's losing finalist, if the Romanian fails to reach the quarter-finals.
Maria Sharapova saved two break points in the third set to get past Dominika Cibulkova 3-6, 6-4, 6-2.
Rafael Nadal without a doubt is King of Clay.
Nishikori dropped the first set but mounted an impressive comeback to secure a hard-fought 6-7, (4-7), 7-5, 6-4 victory.
US Open champion Sloane Stephens will play France's Caroline Garcia for a quarter-final place.
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.
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