WATCH the Italian Open LIVE in Australia on beIN SPORTS | Sign up here

The Serbian, who has not played since the semi-finals in Monte-Carlo, made a slow start, falling 1-3 behind in the first set, but recovered to take the first match.

Moutet could not regain his level, and Djokovic dropped only one set as he cruised through the second match to advance after one hour and 26 minutes.

Djokovic now has 23 wins in ATP-1000 events since turning 35. He eclipses John Isner (22) for the outright second most wins in such tournaments since the introduction of the format in 1990; only Federer, with 51, has more.

The Serbian will have the opportunity to clinch his 1100th match win in the third round as he chases his first trophy of the season. 

Djokovic, a six-time champion in Rome, will take on Alejandro Tabilo in the third round after the Chilean beat Yannick Hanfmann 6-3 7-6 (7-4).