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Djokovic, back in his stride after his shock second-round defeat to Bulgaria's Grigor Dimitrov in Madrid last week, had too much power and control for the 23rd-ranked Dolgopolov and brushed him aside in exactly an hour after the day's play had been briefly delayed by rain.
The pony-tailed Dolgopolov, wearing a custard-yellow shirt, missed two chances to break Djokovic in the sixth game of the second set and surrendered the final game to 15 when the Serbian hit a forehand winner.
"That is exactly what I was looking for in my game," Djokovic told Sky television.
He refused to dwell on his Madrid defeat, when the crowd turned against him after he questioned several line calls.
"What happened on the court that night, I will forget about it," said Djokovic, who now faces Tomas Berdych after the Czech sixth seed defeated South African Kevin Anderson 7-5 6-2.
Berdych came back from a break down in the opening set on the Foro Italico clay to level at 4-4 and never looked back.
The 27-year-old Czech, though, will have to step up his game against Djokovic who has beaten him 13 times in 14 previous meetings.
Defending champion Rafa Nadal, hoping to get back into the world's top four with a good run in Rome, was playing Latvian qualifier Ernests Gulbis in the third round later on Thursday, while last year's women's winner, Maria Sharapova, was facing American Sloane Stephens.
