New Paris St Germain signing Mbappé, who joined the capital club earlier on Thursday, wrapped up the victory in added time after the teenager came on as a late substitute.
Antoine Griezmann had put the home side in front after 14 minutes, beating goalkeeper Jasper Cillessen with a left-foot shot from inside the area after a quick one-two with fellow striker Olivier Giroud.
Midfielder Lemar, arguably the best player on the pitch, doubled the advantage by firing a superb half-volley into the top corner of the net from 20 metres after 73 minutes before adding a third from close range in the 88th.
The Dutch, who hardly created a chance, played the last 30 minutes with 10 men after midfielder Kevin Strootman was sent off for two yellow cards in quick succession.
France now top Group A on 16 points from seven matches, three points ahead of Sweden, who lost 3-2 in Bulgaria. The Dutch are six points off the top in fourth place, two points behind third-placed Bulgaria.
The winners of the nine groups qualify directly for Russia while the best eight of the second-placed teams take part in two-leg playoffs for four more places.
France, who had looked sluggish until Griezmann showed them the way, then stepped up a gear and thrilled their fans, notably with fine midfield moves by Lemar and blistering runs from winger Kingsley Coman.
The visitors, who have now lost their last four games against France, looked clumsy at the back, short of ideas in midfield and toothless up front.
They threatened only once, when a header from close range by veteran winger Arjen Robben was headed out by France defender Samuel Umtiti 20 minutes from time.
The 18-year-old Mbappé, whose move to PSG from Monaco on loan with an option for a permanent deal was concluded shortly before kickoff, made the most of his few minutes on the pitch, concluding one his trademark, zippy runs with his first goal for France on his fifth appearance.
"This is just a step forward but it was a solid performance", said France coach Didier Deschamps, whose men bounced back from a 2-1 defeat in Sweden in their previous qualifier in June featuring an embarrassing blunder from goalkeeper and captain Hugo Lloris.
'Not good enough'
"They were down to 10 men but, still, we showed good things with the ball and produced a strong, collective performance," Deschamps added.
"There are still nine points to play for and we are not worrying about the others, even if the fact that Sweden lost in Bulgaria is not a bad thing."
Dutch coach Dick Advocaat, on a mission to heal the pride of a team he has managed in the past, admitted France were just too strong.
"France's win is well-deserved," he said. "They have very good players and we were simply not god enough.
"When you look at the players who were on the bench and those who were not even here tonight, you can only think that this France team can go a long way.
"As for ourselves, it's not over. If we win our last three games, we can still make the playoffs."
Les Bleus face a relatively straightforward match when they host Luxembourg in Toulouse on Sunday. Sweden visit Belarus, while the Dutch and Bulgarians also meet.