Griezmann and Kylian Mbappe - who, incidentally, was marginally offside when Pogba played his pass - both got in behind their markers. But after a consultation with the VAR, Cunhua pointed to the spot.
With the world watching him in a World Cup opener against Iceland, the normally brilliant Messi struck a weak spot kick that was saved, leaving Argentina with a disappointing 1-1 draw.
The lingering controversy didn't last long.
Minutes later, they drew level through a penalty of their own - Samuel Umtiti with a weird handball gifting Aston Villa's Mile Jedinak the chance to level things up.
Jose Mourinho insists Paul Pogba should be stripped of his winning goal in Saturday's World Cup clash against Australia.
Risdon believes he got the ball first before touching the Les Bleus striker.
It's the ideal start for France, whose ambition is to finish at the top of a group that also includes Peru and Denmark.
"Yesterday is yesterday, the game is gone, and now we have to look forward to Denmark on Thursday".
In the now standard ritual when a new ball is released, the goalkeepers had a good old moan about the ball for the World Cup in Russian Federation as soon as they got their hands on it.
Substitute Tomi Juric was caught walking instead of closing down passing lanes when the ball was played to the feet of an unmarked Pogba.
Critics of the system say it takes spontaneity out of the game, but the VAR interventions at this year's World Cup have so far been quick and "painless". The first stoppage in play after the incident was roughly 25 seconds after it.
"When the referee went to check out the video, I already had the penalty [in my mind] - I was focused on taking it".
The game finally burst into life 10 minutes into the second period with Griezmann's historic goal.
A good result for France, but this dynamic attack was anything but.
It is the first time that VAR has been used at the World Cup, and there will be relief that the decision made was probably correct one, though that did not social media to complain that the wrong decision had been arrived at, amongst other criticisms.
"It was nothing to do with the fact we have a lot of young players", said Deschamps in defence of a squad which, after Nigeria, is the youngest at the World Cup.
World Cup match report Costa Rica v Serbia 17 June 2018
By the full-time whistle, Brazil had piled up 21 shots (just four on target) compared to just six from Switzerland (two). Navas also stopped Milinkovic-Savic's bicycle kick in front of goal in the 42nd minute, but it was ruled offside.