Giroud swept in the winner from a Benjamin Mendy cross in the 75th minute for his first goal in 11 games in a France shirt, after the Chelsea striker went through the entirety of his country's triumphant campaign in Russia without scoring.
On their first appearance on home soil since the World Cup, Mbappe had earlier put France ahead in an explosive performance from the 19-year-old, before Ryan Babel briefly restored parity in the second half.
The Stade de France exploded in celebration at Giroud's winner in a game that had a competitive edge as part of UEFA's new Nations League.
"The victory was the most important thing, so we can have a great party," coach Didier Deschamps told television station M6.
"I am really pleased for Olivier. Strikers can have periods like that where they are not as efficient, but he is useful in our build-up play, he scored a lovely goal, and on top of that it gave us the victory."
The day after beating Croatia 4-2 in the final, Les Bleus paraded hurriedly down the Champs-Elysees Avenue in Paris en route to a reception hosted by President Emmanuel Macron.
The rushed nature of those celebrations disappointed the estimated 300,000 fans who took to the streets, and so this time the victorious squad were presented one by one to supporters after the final whistle.
"Now is the time to have a party," Paul Pogba told M6.
"When we came back to France it was very short. There was all the security around the bus and we couldn't really celebrate with the public.
"This time we are at the Stade de France, it's full, it's beautiful."
The France starting line-up was the same as that in Thursday's 0-0 draw with Germany in Munich, meaning the only change from the World Cup final was in goal, with Alphonse Areola replacing the injured Hugo Lloris.
- Spine-tingling -
The teams were greeted by an enormous banner that read 'world champions' and covered the pitch, before a spine-tingling version of the French national anthem.
Mbappe forced a good save from Netherlands goalkeeper Jasper Cillessen inside 50 seconds, and his performance here showed why he is tipped as a future Ballon d'Or winner.
He got the breakthrough in the 14th minute as he turned in a ball driven across the box by Blaise Matuidi for his eighth international goal in 2018.
The hosts looked in complete control against a Dutch side rebuilding under Ronald Koeman after failing to qualify for Euro 2016 or the World Cup.
It took the visitors 66 minutes to seriously threaten, as Georginio Wijnaldum found himself in behind the defence only to drag his shot wide.
But the Dutch were level just a minute later, Kenny Tete delivering a cross from the right for Babel -- unmissable with his hair dyed red - to convert.
Giroud got the winner though, his 32nd for his country seeing him move one clear of Zinedine Zidane's tally for France.
After drawing in Germany, France are in control in the three-team Group 1 of League A in the Nations League, with the group winners going through to the four-team finals next June.
But for them the evening was always about the post-game festivities first and foremost.
(This story has not been edited by Devdiscourse staff and is auto-generated from a syndicated feed.)