Murray now owns a dominating 10-0 start on the dirt as he competes at the Foro Italico after making a late decision to see how his body had held up after his stunning Madrid Open win on Sunday over Rafael Nadal.
"My legs were a bit tired at the start but they started to feel better after a few games," said Murray. "I played a good match.
"He (Chardy) has a big serve, it was tough for me. But I hung in, moved well and didn't give him loads of opportunities. I served well throughout the match.
"I'm happy with how I adjusted to conditions, I made it difficult for him to win free points.
"I don't know how my body will feel over the next days, but I'll try to spend as much time recovering and resting as possible."
Nadal, his seeding down to fourth, began his title defence and the quest for a record eighth Rome trophy as he crushed Turk Marsel Ilhan 6-2, 6-0 in barely one and a quarter hours.
Third seed Murray is bidding for a potential pre-Roland Garros trophy hat-trick after winning the first clay honour of his career in Munich and following up with a huge title success in Madrid at the expense of Spain's king of clay.
The soon-to-be 28-year-old Scot is playing Rome for the tenth straight edition, now standing a level 9-9 over his career at the venue.
He reached the quarter-finals in 2014, losing to Nadal in three sets.
Murray beat Chardy in 84 minutes with six aces and three breaks of the Frenchman's serve, leading 6-1 in the series. The seed's victory was his 31st of the season against five defeats.
Japanese fifth seed Kei Nishikori won his opining test four days after falling in a Madrid semi-final to Nadal, with Asia's top player defeating Czech Jiri Vesely 7-6 (7/3), 7-5.
American John Isner continued to play outside of his comfort zone, the 16th seed sending over 11 aces in a 7-6 (8/6), 6-4 defeat of Argentine Leonardo Mayer.
Spain's Guillermo Garcia-Lopez accounted for Ukrainian qualifier Alexandr Dolgopolov 6-4, 6-3.
In the women's draw, second seed Simona Halep made up for last week's surprise opening exit in Madrid, defeating American Alison Riske 6-3, 6-0 for a place in the third round.
Halep said that her physical niggles of last week are no longer an issue.
"I feel good and I have no pain anymore, just a little bit of contraction in the back muscle. I can run, I can play, I can do everything," said the 2014 French Open finalist.
Two seeds lost as Russian Daria Gavrilova put out seventh seed Ana Ivanovic 5-7, 7-6 (7/2), 7-6 (9/7) barely a month after upsetting Maria Sharapova in an opening round in Miami.
Serb Bojana Jovanovski defeated 15th seed Madison Keys 6-4, 1-6, 6-3.