Djokovic needs to reach the semi-finals in Rome to ensure Daniil Medvedev cannot usurp him atop the ATP rankings next week, and he made a solid start with a 6-3 6-2 victory over another Russian in the second round.
Karatsev did initially pose a threat, with both players breaking at the first opportunity, but Djokovic's superiority gave him the edge in the first set and then saw him cruise in the second.
Djokovic – who will face either Stan Wawrinka or Laslo Djere next – acknowledged he undoubtedly benefited from Karatsev's wastefulness, however.
"You never know with him," Djokovic said. "If he's feeling the ball, he can be very dangerous because he stays so close to the line, puts pressure on his opponents.
"He was missing a lot of balls today, though. He gave me a couple of breaks there in the first and second sets, but I'll take this win for sure.
"It's a straight-sets win against a quality opponent, and I'm looking forward to the next challenge."
Fifth seed Casper Ruud also progressed to the last 16 but was tested by Botic van de Zandschulp, with the Norwegian eventually coming through 6-7 (4-7) 6-2 6-4.
But Andrey Rublev, who had won six of his previous seven matches, was a surprise second-round casualty as he fell to Filip Krajinovic in straight sets, with the Serbian claiming a 6-2 6-4 win.
Canadians Felix Auger-Aliassime and Denis Shapovalov were the other seeds to reach the last 16 on Wednesday. The former was pushed hard by Alejandro Davidovich Fokina in his 4-6 7-6 (7-2) 6-2 success, while the latter could face Rafael Nadal next up.
Meanwhile, across seven first-round matches, Cameron Norrie, Jannik Sinner and Diego Schwartzman were the biggest names to advance, though 11th seed Hubert Hurkacz was dumped out by the unseeded David Goffin.