In a pulsating semi-final worthy of the teams' reputations, Umtiti rose high at the near post to head an Antoine Griezmann corner past goal-keeper Thibaut Courtois.
It was enough to take France to the final for the first time since 1998, when they won their only World Cup as hosts of the tournament.
Belgium, playing in their second World Cup semi-final after one in 1986, piled on the pressure and came close with a Marouane Fellaini header in the 65th minute and a string of other chances.
But they could not find an equaliser despite having netted 14 times in their previous five games in the tournament.
At the final whistle, the France substitutes ran on the pitch to celebrate with the players, while manager Didier Deschamps was mobbed by his staff before dancing around in a circle.
Twenty years ago, France won the World Cup for the first and only time, in their history at home in Paris with a 3-0 win over Brazil.
That team was Captained by Deschamps, who is now aiming to emulate Brazilian Mario Zagallo and Germany's Franz Beckenbauer by winning the competition as both a player and manager.