Just before the pause, Olivier Giroud effectively ended the contest with France's third.
The 32-year-old struck his 34th international goal to draw level with David Trezeguet as the country's third highest scorer.
Only Michel Platini with 41 and Thierry Henry with 51 goals are ahead of the Chelsea striker.
"I admire Olivier a lot," said France defender Benjamin Pavard. "He gets a lot of criticism but he always turns up and he scores goals. He's a great professional and a really good player."
Giroud, who equalled Trezeguet's mark on his 88th appearance for France, was one of the key players during the surge to the 2018 World Cup despite receiving flak from the pundits for his lack of goals during the Russia campaign.
"There are two ways to react to all the complaints," said Giroud. "You can listen to them and let it get to you ... or you can listen to them and try and use it all positively and help the team. I've been trying to help the team."
Kylian Mbappé scored France's fourth on 87 minutes.
Thomas Lemar's challenge on Eugeniu Cebotaru fed the Paris Saint-Germain forward who slotted past Moldova goalkeeper Alexei Koselev.
The hosts claimed a consolation goal in the dying seconds when midfielder Vladimir Ambros tapped in a rebound off the post.
"We played a very consummate first-half in terms of control and attacking organisation," said France coach Didier Deschamps. "The second half was less fulfilling due to the substitutions."
France play their second match in Group H on 25 March at the Stade de France in Saint-Denis against Iceland. Moldova travel to Eskisehir to face Turkey.
Deschamps added: "The second game comes around quickly and we have do it again but we've opened our campaign well."