Nadal, the world No 2 and seven-time champion in Rome, was in devastating form in the Italian capital, brushing aside Damir Dzumhur of Bosnia and Herzegovina 6-1, 6-0 in just over an hour.
Seven-time champion Nadal - seeking to reclaim the number-one ranking he conceded last week - hammered Dzumhur 6-1 6-0 after Thiem had gone down in three sets to Fabio Fognini, the Austrian smashing a racquet in anger during an intense contest.
Nadal was at his ruthless best against Damir Dzumhur, converting five of eight break points on the way to a dominant 6-1, 6-0 victory.
Wozniacki eliminated Belgian qualifier Alison van Uytvanck 6-1, 6-4, and three-time Rome champion Maria Sharapova came back to beat Dominika Cibulkova 3-6, 6-4, 6-2.
The 31-year-old, whose 21-match unbeaten run on clay ended last week, had a first-round bye and will play Denis Shapovalov or Robin Haase next.
The 16-time Grand Slam victor next takes on either Canadian teenager Denis Shapovalov or Robin Haase.
Rafael Nadal and Novak Djokovic remain on course for a semi-final showdown at the Italian Open after both players eased into the third round yesterday. So I'm disappointed that I lost, obviously.
"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.
Bulgarian third seed Grigor Dimitrov also suffered an early exit, going out to Japan's Kei Nishikori after a marathon 6-7 (4/7), 7-5, 6-4 battle.
With the score at 6-3, 3-6, 5-5 and serving at 30-30, Pliskova had an overhead smash incorrectly called out, and after the umpire, Marta Mrozinska, could not find the ball mark the original call stood.
The controversial shot came in the third set with the Czech serving at 5-5 (30/30).
Maria Sakkari of Greece rallied past sixth-seeded Karolina Pliskova 3-6, 6-3, 7-5.
Instead of shaking hands with the umpire after the match, Pliskova first put her hand out before beating up the chair.
Fognini had his home-country crowd behind him, and when he went three set-points up against Thiem, it was clearly too much for the Austrian to take. "That was the way that I want to play".
"I like to slide on the clay and today was easy for me". I don't know how many mistakes I made, but not many.
Quarter-final appearances in the Rio Open, Mexican Open, the Monte Carlo Open AND the Barcelona Open in the opening months of the season has kept Thiem at a consistent eighth place in the world rankings, but a slight drop from his previous peak position of number four in November 2017.
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.