World number one Djokovic won 5-7 6-2 6-3 but was made to work hard after his Brazilian opponent, ranked 68th, played a flawless opening set with his left-handed serve and powerful forehand repeatedly troubled the holder.
"He (Bellucci) kept me off balance with the variety on his serve," Djokovic said. "I couldn't quite find the right position where to stand on the return."
Once the Serb broke in the fourth game of the second set he relaxed and took control, running Bellucci all over the court with precise ground strokes and impeccable backhand drop shots.
"It was a hard-fought match and I have to give him credit for the way he played," added Djokovic.
He next meets Japan's fifth-seeded Kei Nishikori, who beat Djokovic's compatriot Victor Troicki 6-4 6-3.
Fourth seed Nadal, who has struggled to find his best form this season in the wake of the wrist injury and appendicitis issues that undermined his performances last year, was imperious against the big-serving American and triumphed 6-4 6-4.
He did not face a single break point and won 90 percent of his first-service points.
ALMOST PERFECT
"I was almost perfect," Nadal told Sky Sports Italia. "It was a good match, I'm satisfied."
The Spaniard, who fell to seventh in the rankings after Sunday's Madrid final defeat by Andy Murray, looked to be back on the path to discovering his best claycourt form.
The warm weather made the court faster and Nadal's top-spin forehand forced Isner on the defensive, something the statuesque American does not handle well.
Nadal, a seven-time champion in Rome, will now face Stanislas Wawrinka, who beat Dominic Thiem 7-6(3) 6-4 to record consecutive victories for the first time since February.
Second seed Federer appeared to be heading for an easy win against Anderson as he broke early in both sets and held two match points on serve, leading 5-2 in the second set.
Anderson valiantly fought back to level, however, before losing the last two games and the match 6-3 7-5.
The Swiss will now face Tomas Berdych who was stretched to the limit by home favourite Fabio Fognini. The sixth seeded Czech won 6-3 3-6 7-6(2) to reach his ninth quarter-final of the year in as many tournaments.
Seventh seed David Ferrer crushed fellow Spaniard Guillermo Garcia-Lopez 6-1 6-3 and will play Belgian David Goffin who had a walkover when third seed Andy Murray withdrew with fatigue.
SHARAPOVA FAVOURITE
In the women's event, Maria Sharapova came back from a 3-1 first-set deficit to beat Bojana Jovanovski 6-3 6-3.
The third-seeded Russian, a Rome winner in 2011 and 2012, has taken up the favourite's mantle after Serena Williams withdrew due to a right elbow injury.
Fourth-seeded Czech Petra Kvitova was too powerful for former world number one Jelena Jankovic, hitting 23 winners in a 6-3 6-2 win, and faces Carla Suarez Navarro in the last eight.
Canada's sixth seed Eugenie Bouchard double faulted when she had match point in the third set tiebreak before losing a three-hour battle to Spaniard Suarez Navarro 6-7(2) 7-5 7-6(7).
Romanian second seed Simona Halep beat Venus Williams 6-2 6-1 in just over an hour and next meets compatriot Alexandra Dulgheru.
(Reporting Jacopo Lo Monaco; Editing by Toby Davis)
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