Umtiti headed home a corner from Antoine Griezmann in the 51st minute to send the French team into wild celebrations at the St Petersburg on Tuesday.
This is the third time that France have reached the world cup final in 20 years and would now face either England or Croatia in the final in Moscow.
Goalkeepers Hugo Lloris and Thibaut Courtois both made smart saves to make sure an intriguing game remained scoreless at the interval.
The impressive Mbappe was unleashed from the very beginning as he had a brilliant touch to get past Vertonghen and Dembele but his cross was well dealt with.
Belgium then went into a period of dominance as Hazard looked bright in the opening stages, beating defenders and testing the keeper.
Lloris’ full-length dive kept out a first-time strike from Tottenham colleague Toby Alderweireld, while Courtois reacted quickly to block Benjamin Pavard’s attempt from a tight angle at the other end.
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Both teams went into the break level but France needed just six second-half minutes to get what turned out to be the decisive goal.
After Vincent Kompany’s block turned away Giroud’s shot, Griezmann’s inswinging delivery to the front post was turned in by Umtiti, who beat Marouane Fellaini to head beyond Courtois.
That was Umtiti’s third international goal and a crucial one at that.
Belgium pushed hard for an equaliser but Roberto Martinez watched on as his team suffered their first defeat in 25 outings, ending their hopes of winning the tournament for the first time in history as their so-called golden generation came up short.
Didier Deschamps would be looking to emulate Mario Zagallo and Franz Beckenbauer by winning the World Cup as both a player and manager.