It was a spirited display from Brazil, which managed to pull a goal back after going 2-0 down in the first half, and almost equalized in the dying moments when Neymar forced a fingertip save from Belgian goalkeeper Thibaut Courtois.
Neymar played the entire 90minutes, as Belgium beat the South Americans 2-1 on Friday night.
England face Croatia in the tournament's other semi-final clash after they advanced by easing past Sweden 2-0 in the last eight.
That leaves perhaps the most wide-open World Cup of modern times heading towards the final week, and England manager Southgate has called on his team to take advantage. "If you say losing means we haven't achieved anything, then I can't understand you".
Mbappe has been one of the standout stars of France's surge to the final four in Russian Federation, scoring three goals and turning in a series of electrifying performances.
- Why has World Cup been full of surprises? Marouane Fellaini and Nacer Chadli came off the bench to help complete a stunning three-goal turnaround in the final 21 minutes. We've built that and to get through the two games we've had this week needed all of that because we're not the finished article. I'm very happy to be part of this team, I'm proud of all the players.
Five-time champions Brazil had arrived in Russian Federation with high hopes of putting the humiliation of their 7-1 semi-final thrashing on home soil by Germany four years ago behind them, but were instead sent packing by a clinical Belgian outfit.
With one match to play until the semifinals, it feels like the tournament is wide open. Although an exceptional start to next season from Messi or incredible finish to the World Cup from someone like Neymar could make things very interesting, the only way I could really see Ronaldo relinquishing his crown is if Kane or Modric inspire their country to glory in Russian Federation.
"It is freakish to have Thierry against us in this match", Giroud told reporters.
Neymar was personally tipped for glory in the competition but endured a hard tournament, scoring twice for Brazil but also receiving severe criticism from around the world as a result of his perceived tendency to dive and exaggerate injuries.