- Kylian Mbappé (55' Pen)
- Konstantinos Mavropanos (69')
Mbappe netted a second-half penalty to become the best French scorer over a season with 54 goals for club and country, beating the mark set by Just Fontaine in 1957-58.
It also helped the Paris Saint-Germain forward to level with Norway and Manchester City striker Erling Haaland, who will have the opportunity to finish top scorer among those playing in the five top European leagues when his national team take on Cyprus on Tuesday.
The result left France top of Group B with 12 points, six ahead of second-placed Greece, who had Konstantinos Mavropanos sent off in the second half, after Mbappe's goal.
"It was a long season for the players," said France coach Didier Deschamps. "We did what we had to to win this game even if we can regret we did not score another because you never know what can happen late in the game.
Randal Kolo Muani had a clear chance in the 25th minute with a downward header from Mbappe's cross but his attempt went just wide.
It came after earlier opportunities for Mbappe and Kingsley Coman, but the offensive trio hit a brick wall.
After having three penalty claims denied, Les Bleus had another chance, only for Jules Kounde's volley to be tipped away by Odysseas Vlachodimos.
The hosts were finally awarded a penalty early in the second half after Griezmann, looking to connect with a cross from the left, was hit in the head by Mavropanos.
Vlachodimos, however, parried Mbappe's spot kick, but it had to be taken again as the Greek keeper had left his goal line too early.
Mbappe found the top corner on his second attempt 10 minutes into the second half to score his 40th goal in his 70th international appearance, and Greece's hopes were further dashed when Mavropanos picked up a straight red card when he took down Kolo Muani, who was rushing towards the goal.
"We wanted to follow up on our win against Gibraltar, in front of our crowd," said midfielder Eduardo Camavinga, referring to France's 3-0 win on Friday.
"We knew they were a tough nut to crack but we did the job, three points without conceding a goal. Now, straight to holidays."
After Saturday's 3-0 win against Gibraltar, France have now scored nine goals and kept clean sheets in all their four qualifying games.
They next face Ireland at home on Sept. 7 while Greece will travel to the Netherlands.
- Antonio Miguel Mateu Lahoz