The Spaniard, a seven-time champion in Rome, swept Djokovic aside in the semi-finals of the Madrid Masters last week before going on to secure the title.
Nadal improved his record on clay this year to 17-0 with a 6-3, 6-4 victory over American Jack Sock, the 13th seed.
Serbia's Novak Djokovic returns the ball to to Spain's Roberto Bautista Agut during their match at the Italian Open tennis tournament, in Rome, Thursday, May 18, 2017.
Djokovic, beaten in the final by Britain's Andy Murray past year, will now face either Argentina's Juan Martin del Potro or Japanese seventh seed Kei Nishikori.
"I felt that the start of the season went really well for me this year", Djokovic said at a press conference from Foro Italico where he will play the Masters 1000 tournament in Rome, according to the ATP official website.
Fourth-seeded Nadal broke Sock's serve twice in the second set and served out the match to set up a last-eight meeting with Dominic Thiem, who was beaten by Nadal in the Madrid Open final last week. "I was very happy with the performance".
"I have been doing my best to optimise my game and get it to the highest possible level", said Djokovic, who surprisingly parted company with his coaching staff earlier this month.More news: Senate chairman: Flynn has not responded to subpoena
"I played a more aggressive game and I m serving better".
"It s coming at the right time, we re getting closer to Roland Garros".
The eighth-seeded Austrian was forced to save three match points before battling to a 3-6 6-3 7-6 (9/7) win over another American, Sam Querrey. All the players are looking to raise their game for Paris.
John Isner defeated third seed Stan Wawrinka 7-6 (7/1) 6-4 to set up a rare clay-court quarter-final against sixth seed Marin Cilic, who beat David Goffin 6-3 6-4.
"It s so different when you re talking about it or when you re playing it", she said.
Home favorite Fabio Fognini, who saw off top-seeded Andy Murray on Tuesday, lost 6-3, 6-3 to Alexander Zverev, who will play fifth-seeded Milos Raonic in the quarterfinals after the Canadian beat Tomas Berdych 6-3, 6-2.
Halep surged into the last-four for the third time after a 6-2, 6-4 win over Estonian qualifier Anett Kontaveit.