Les Bleus had failed to win in their previous five games, dating back to their opening Euro 2020 triumph over Germany.
Didier Deschamps’ side had drawn with both Bosnia-Herzegovina and Ukraine during this international break but found their form in Lyon led by Griezmann.
The Atletico Madrid forward moves equal with Michel Platini in third on France’s all-time scoring charts with 41 strikes, behind only Thierry Henry (51) and Olivier Giroud (46).
“Even if we didn’t do everything well, today there was more determination and from there, the technical quality is there,” Deschamps told TF1.
“It was a very important result, but the job will have to be finished in November. We have never stayed for such a long period (without a win), it can happen.
“We must therefore appreciate this victory and especially during the last two qualifying matches in November, finish the job.”
Deschamps deployed Griezmann alongside Karim Benzema and Anthony Martial in an attacking trio without injured forward Kylian Mbappe.
Griezmann’s quality was the key, poking home the opener in the 25th minute, before firing in an angled effort eight minutes into the second half.
“Maybe we found a system that suits us best,” Deschamps said. “We’ll see. It’s the coach who’ll decide. But tonight, we were strong.
“Five draws was a long time. We wanted to win and we did it in the right way.”
Elsewhere, Bosnia-Herzegovina were held 2-2 by Kazakhstan, helping Les Bleus open up their lead in Group D.
Portugal continued their strong form with a 3-0 win at Azerbaijan without Cristiano Ronaldo, while Republic of Ireland drew 1-1 with Serbia.
Euro 2020 semi-finalists Denmark maintained their perfect qualifying record, having also still not conceded a goal, with a 5-0 win over Israel, while Scotland shocked Austria 1-0 away.
Louis van Gaal’s Netherlands won 6-1 over 10-man Turkey, while Norway kept the pressure up as Erling Haaland netted a treble in a 5-1 home win over Gibraltar.
Croatia triumphed 3-0 over Slovenia, while Russia got past Malta 2-0 to stay level on points at the top of Group H.