The Atletico Madrid attacker opened the scoring in the 24th minute of the Group H encounter before crossing for Raphael Varane to double the scores three minutes later.
Olivier Giroud equalled David Trezeguet as Les Bleus’ third highest scorer of all time with his 34th international goal nine minutes before the break and Kylian Mbappe completed the rout with three minutes left, before Vladimir Ambros claimed a late consolation for Moldova.
Left-back Layvin Kurzawa was the only member of the starting lineup without a World Cup medal as Bayern Munich winger Kingsley Coman pulled out during the warm-up with a muscle issue and was replaced by Blaise Matuidi.
“We played a very consummate first half in terms of control and attacking organisation. The second half was less fulfilling due to substitutions,” said coach Didier Deschamps.
“We’ve opened our campaign well and the second game comes around quickly. In three days we have to do it again,” Deschamps added ahead of facing Iceland on Monday.
Griezmann had the best of the early chances but his effort from far out failed to threaten Alexei Koselev in the home side’s goal after 17 minutes.
The shaggy-haired wide-man scored his 27th goal for France seven minutes later, Manchester United playmaker Paul Pogba picking Griezmann out inside the box with a perfectly timed chip before he hit a lob first time to beat a flat-footed Koselev.
Griezmann then turned provider, his corner finding center-back Raphael Varane, who headed to double the visitors’ advantage at the Zimbru Stadium.
Giroud put to bed when he met late call-up Matuidi’s cross a left-footed volley.
Giroud missed an opportunity to move ahead of Trezeguet’s record 34 goals shortly after the break when his header from a Griezmann cross flew past the post.
Pogba could have added a second assist to Griezmann’s account but his header was parried away superbly by Koselev on 70 minutes, and the Manchester United man went close again with 11 minutes left when his shot could only find the side-netting.
Kylian Mbappe succeeded where Pogba failed on 87 minutes.
Lemar’s challenge on Eugeniu Cebotaru fed the Paris-Saint Germain forward who easily beat keeper Koselev.
The hosts claimed a consolation goal with 90 seconds of normal time remaining when midfielder Ambros capitalised on a rebound off the post to fire past Hugo Lloris.
Next up for France is Iceland, while as Moldova, who are yet to qualify for an international tournament, head to Turkey.
AFP