Fittingly, a defender settled the affair six minutes after the restart.
Vincent Kompany conceded a corner when he blocked Olivier Giroud’s shot on the turn.
Griezmann took the kick from the right and amid the habitual penalty area scuffling, Samuel Umtiti broke free just ahead of Marouane Fellaini to power his header past the Belgium goalkeeper Thibaut Courtois.
“The difference between defeat and winning was down to one dead ball situation,” said Belgium coach Roberto Martinez. “That’s how close the game was. France wanted to exploit the counterattack with the pace of Griezmann and Mbappé and we controlled that extremely well.”
Belgium, unsurprisingly enjoyed the lion’s share of possession but found the French rearguard in mean mode.
“You have to give France credit for the way they defended,” added Martinez. “They even got their attacking players to drop deep. That gave us a lot of respect but we couldn’t find that little bit of magic in front of goal or a little bit of luck and that was the difference, having a little bit of luck at certain moments in both boxes.”
After the 4-3 goalfest in the last 16 against Argentina, France have kept consecutive clean sheets against Uruguay and Belgium sides which have been robbed of key players through injury or suspension.
Uruguay striker Edinson Cavani could not play in the quarter-final because of a calf strain while Belgium’s Thomas Meunier was ineligible for the semi-final after picking up too many yellow cards.
But France too lost key players. Blaise Matuidi returned from suspension to add more industry to the running of N’Golo Kanté and Paul Pogba’s physicality. Belgium’s maestros, Eden Hazard and Kevin de Bruyne often found themselves outnumbered and four goal striker Romelu Lukaku was unable to manoeuvre an opening.
The victory allows France coach Didier Deschamps the chance to become only the third man after Brazil’s Mario Zagallo and Germany’s France Beckenbauer to win the World Cup as a player and as a coach. Only Croatia or England can stop that personal accolade.
Deschamp’s side, however, will enter the final at the Luzhniki Stadium on Sunday as favourites after containing Belgium’s firepower. It will be an opportunity, says Deschamps, to purge their loss in the European championships final in 2016.
"Finals have to be won because we have still not got over the one we lost two years ago. I am very happy for my players. They are young but they have character and a winning mentality."