The Briton's second career triumph, and second of the season, was particularly resonant coming in Max Verstappen's backyard with more than 100,000 mostly orange-shirted fans cheering for Red Bull's championship leader.
Norris took the chequered flag a mighty 22.896 seconds ahead of Verstappen, the biggest margin so far this year, but is still a huge distance behind the triple world champion with nine races remaining.
"I've been working hard the whole year and I'm still 70 points behind Max. So it's pretty stupid to think of anything at the minute," he said when asked about the title.
"I just take one race at a time and just keep doing what I'm doing now because there's no point to think ahead and think of the rest."
No Formula One driver has ever overcome a deficit of such a magnitude but Red Bull's motorsport adviser Helmut Marko was concerned anyway.
"As Max said before the summer break, the team has to work harder and must find improvements because like that his championship is in threat," the Austrian told the website.
Norris clawed back eight points on Sunday, one for fastest lap, but he will need Verstappen to start squandering many more over the coming months and the Dutch driver does not have a history of doing that.
McLaren teammate Oscar Piastri will also have to take points off Verstappen, to boost Norris's chances, but the Australian finished fourth on Sunday.
It would also help if Mercedes, winner of three races this season, and Ferrari, twice triumphant, pushed the Red Bull further down the field as well.
McLaren are only 30 points adrift of Red Bull in the team battle, however, and looking increasingly like they could win their first constructors' title since 1998.
Sunday's race also allowed Norris to slay one particular bugbear, it being the first time he had won a grand prix from pole position after costly mistakes in the past by both driver and team.
He was also willing to concede that his McLaren, upgraded for the first time since Miami in May, was the quickest car out there.
"Today, this whole weekend, I think we've had the best car. I think we've, on average, had the best car for sure," he said.
"We worked hard over the summer break to just try and take a step back and reset and go again. So yes, we've had a great car.
it's still a long way to go. So we still have to keep working hard because this is just Zandvoort.
"Monza is a completely different circuit. So we'll keep our heads down and keep chipping away."
The championship continues next weekend with the Italian Grand Prix outside Milan.
