Defender Umtiti headed home a corner from Antoine Griezmann in the 51st minute to settle the all-European tie, booking Les Bleus a trip to Moscow and a clash against either Croatia or England.
Goalkeepers Hugo Lloris and Thibaut Courtois both made smart saves to make sure an intriguing game remained scoreless at the interval.
However, Umtiti popped up with the game's telling moment early in the second half, nodding the ball home to score his third international goal.
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.
Beaten finalists at Euro 2016 on home soil, France will aim to go one better in Russia and emulate the successful squad of 1998 which included Didier Deschamps, who could emulate Mario Zagallo and Franz Beckenbauer by winning the World Cup as both a player and manage
