Defending champion Elina Svitolina returned to the Italian Open final with a comfortable 6-4, 6-3 win over 26th-ranked Anna Kontaveit.
Nadal and Djokovic have played each other 50 times but their last meeting came more than a year ago, when Nadal won in the Madrid Open semifinals.
For a spot in the final, Nadal will play four-time Rome champion Novak Djokovic or Kei Nishikori.
Nadal, who hasn't won the Italian Open since 2013, will next face Fabio Fognini, who beat Peter Gojowczyk 6-4, 6-4 to reach his first quarterfinal in 11 appearances at his home tournament.
The seventh-seeded Indo-French pair lost 6-7(5) 4-6 to their unseeded opponents of Pablo Cuevas and Marcel Granollers in one hour and 32 minutes.
Halep needed to reach the quarterfinals to progress further than No. 2 Caroline Wozniacki to hold onto the top spot, and she accomplished the first task.
Nadal, a seven-time Rome champion, routed 31st-ranked Damir Dzumhur 6-1, 6-0.
The tournament will mark the 23-time Grand Slam champion's first major since returning to the tour from maternity leave.
The 21-year-old Zverev won his eighth career title and second of the season after also winning the Munich Open last weekend.
Thiem beat the sixth-seeded Anderson after breaking both of his first service games in each set.
Nadal hadn't lost a single set on clay since falling to Thiem at the Rome Open quarterfinals one year ago.
Kiki Bertens beat seventh-seeded Caroline Garcia 6-2, 6-2 to advance to the Madrid Open final on Friday.
Pliskova's only prior victory from a previous seven matches against Halep was in the 2016 Fed Cup.
Novak Djokovic has struggled since returning from a layoff for a right elbow injury and is yet to reach the quarterfinals in the six tournaments he has played this year.
Djokovic lost in the third round in Monte Carlo and in the second round in both Miami and Indian Wells. The 12th-ranked Serb also failed to advance past the last 16 at the Australian Open.
Serena Williams has withdrawn from next week's Italian Open, saying she needs more time to be "100 percent ready to compete."
Top-seeded Simona Halep reached the third round by beating Elise Mertens 6-0, 6-3.
Djokovic broke serve late in each set to get past the 20th-ranked Nishikori after nearly two hours in the Magic Box.
Alexander Zverev defeated three-time former champion Philipp Kohlschreiber 6-3, 6-3 to defend his Munich Open title on Sunday.
Petra Kvitova came from a set down to beat seventh-seeded Mihaela Buzarnescu of Romania 4-6, 6-2, 6-3 in the Prague Open final.
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