• Djokovic reached his 17th successive Rome quarter-final with a 6-3 6-4 win in a tetchy encounter on Tuesday.
• The 27-year-old Briton saved three set points but could do nothing about the fourth as Djokovic wrapped up the opener.
Novak Djokovic criticised Cameron Norrie's behaviour after the Briton hit him with a smash while his back was turned in their Italian Open match.
Djokovic reached his 17th successive Rome quarter-final with a 6-3 6-4 win in a tetchy encounter on Tuesday.
He had already been irritated by the British number one's shouts of "Come on", before being hit in the ankle when he had already given up the point.
"Those are the things we players know are not fair play," Djokovic said.
"It's not how we treat each other, but it is allowed."
Having delayed the start of the match for a few minutes while he was in the treatment room, Djokovic wasted no time in racing into a 3-0 lead before Norrie slowed down his opponent's charge with a couple of holds.
The 27-year-old Briton saved three set points but could do nothing about the fourth as Djokovic wrapped up the opener.
Norrie, seeded 13th, went a break down early in the second and immediately broke back - but in controversial fashion.
Djokovic had already surrendered the point when he hit high to leave Norrie with an open court to put the ball into and was walking away when Norrie fired his smash into Djokovic's left ankle.
Norrie uttered a brief "sorry" and raised his hand in apology, earning whistles from the crowd and a huge glare from a clearly riled Djokovic.
With conditions cool and the mood on court even frostier, Djokovic went on to break to love for 5-4.
Having been made to wait at the start of the match, it was then Norrie's turn to keep Djokovic waiting as he received treatment on court on his hip while the Serb prepared to serve for the match.
Djokovic went 0-30 down but resumed his focus as he sealed victory on his second match point to stay on course for a seventh Italian Open title, with the pair exchanging a tense handshake and no words at the net.
"I have got along very well with Cameron over the years that he's been on tour. He's a very nice guy off the court so I don't understand this kind of attitude on the court," said Djokovic, who faces Danish seventh seed Holger Rune in the last eight.
"He brought the fire and I responded to that. I'm not going to allow someone behaving like this bending my head.
"That's all it is. What happens on the court, we leave on the court and move on."
Russian sixth seed Andrey Rublev was beaten 7-6 (7-5) 4-6 6-3 by German qualifier Yannick Hanfmann after home favourite and eighth seed Jannik Sinner fell 6-7 (3-7) 6-2 6-2 to Francisco Cerundolo of Argentina.
Hanfmann will play third seed Daniil Medvedev after the Russian beat Alexander Zverev 6-2 7-6 (7-3), while Cerundolo will face French Open runner-up Casper Ruud.
Djokovic finding form in time for French Open
Djokovic's preparation for the French Open has been disrupted by injury but he is finding form in time for his bid for a 23rd Grand Slam singles title when it starts on 28 May.
Djokovic missed the recent Madrid Open with an elbow injury and before that had made earlier-than-expected exits from tournaments in Monte Carlo and Bosnia and Herzegovina to leave his clay-court preparations in less than ideal shape in the run-up to the French Open.
He and Rafael Nadal both have a chance to win a record 23rd men's major singles title at Roland Garros, but with the Spaniard having been unable to play since the Australian Open in January because of a hip injury neither is a red-hot favourite to win in Paris.
Spain's US Open champion Carlos Alcaraz, who will take over as world number one from Djokovic when the rankings are updated next week, has been looking good for a French Open challenge after back-to-back titles in Madrid and Barcelona.
However, the 20-year-old suffered a shock last-32 defeat in Rome on Monday by Hungarian qualifier Fabian Marozsan to make his earliest exit in a tournament since October.
Even if Djokovic wins the title in Italy, he will still lose the number one ranking, but he would head to Paris with his clay season back on track.
Against Norrie he was more assured than in the previous two rounds, albeit he was helped by the Briton's unforced error count which reached 29.
"So far, so good," Djokovic said in his on-court interview.
"I'm just glad to overcome today's challenge in straight sets and move on."
He did not give details about what the issue was that he had received treatment for before the match but suggested there was no cause for concern.
"Every day there's something," he added. "Thankfully I was able to play and finish the match and hopefully tomorrow I will feel even better."
Norrie will continue his French Open preparations next week at a tournament in Lyon, where he is the top seed.