The youngest driver in the race, at 20 years old, became the third youngest ever to stand on a grand prix podium -- after Max Verstappen and Lance Stroll -- and also the youngest Briton.
He had been stunned already with fourth place in qualifying at the Red Bull Ring, which became third on the grid when six-times world champion Lewis Hamilton was given a three-place penalty.
He then declared himself lost for words after edging Hamilton off the podium by two tenths when the Mercedes driver collected a five-second penalty for causing a collision with Red Bull's Alex Albon.
"I'm speechless. There were a few points in the race where I thought I'd kind of fudged (messed) it up quite a bit," he said.
To get on the podium, Norris left no margin for error as he set the fastest lap of the race -- letting out wild shrieks of joy, with some words bleeped out, over the team radio when he realised it was mission accomplished.
Lando Norris of Great Britain
Image credit: Getty Images
"There could be nothing better for the entire team, especially after this difficult period," said McLaren principal Andreas Seidl of the team's second podium in three races, albeit separated by seven months.
"I'm looking forward despite social distancing and masks tonight to have a small celebration at least."
Drivers and teams are maintaining social 'bubbles' in the paddock to minimise the risk of the COVID-19 pandemic causing further havoc to a season halted in March, but there was no restraining Norris.
He embraced McLaren Racing chief executive Zak Brown and sprayed fizz at mechanics and team mates.
At a later video news conference Norris had to ask for a change of face mask to be able to breathe, so soaked was it in champagne.
"I really want to give you a hug now, mate, but I can't," said compatriot and 2009 world champion Jenson Button as he conducted post-race interviews at the finish line. "No words. I mean, awesome. A fantastic race."