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.
Rafael Nadal, enjoying his best season on clay in two years, will look to book his place in the last eight later when he meets American Jack Sock, seeded 13th.
The four-time champion edged past local player Roberto Bautista Agut in straight sets (6-4, 6-4) in his R16 match yesterday to continue his quest to hit peak form after parting ways with his coaching team last month. "The last time we played I won in Paris past year, the indoor tournament in Paris", added Isner. "But I ll keep fighting". The 16th seeded Zverev won the first set on a single break of serve and carried the momentum into the second set as he took a 4-0 lead. "It came at the right time, of course". "I went out there with the belief that, if I played well and executed my game plan, that I could walk off that court with a win. What I know for sure is that I'm doing my very best to rediscover myself in a new way and get the new strength and the new skin, so to speak", he explained.
Third seed Stan Wawrinka became the latest high-profile casualty at the Italian Open on Thursday when the Swiss was knocked out in the third round by American John Isner.
Isner next faces another big server in sixth-seeded Marin Cilic, who dismissed ninth-seeded David Goffin 6-3, 6-4. I'm happy I reached the semi-finals in Madrid, which has been my best result this year.
The Austrian fought off a double match point at 4-6 in the tiebreaker, then thwarted a third match point at 6-7 before surviving.
The 20-year-old will now take on fifth seed Milos Raonic, a 6-3, 6-2 victor against the 12th seeded Tomas Berdych.
In the women s tournament, Venus Williams overcame determined Briton Johanna Konta to win their third-round clash 6-1, 3-6, 6-1.
Estonian qualifier Anett Kontaveit, who beat top-ranked Angelique Kerber in the second round, continued her dream debut.
First round: Anette Kontaveit bt Andrea Petkovic 6-3, 6-4; Ekatarina Makarova bt Roberta Vinci 6-2, 6-1; Kiki Bertens bt Monica Nicolescu 2-6, 6-2, 6-1; Daria Gavrilova bt Madison Keys 2-6, 7-5, 7-5.