More than 15 millimetres of rain fell before the chequered flag in Melbourne but the Brit dazzled in the deluge.
He held off a late challenge from Max Verstappen to draw first blood in another white-knuckle battle with the Dutchman.
Norris, 25, said: "To start the season with a win is good but it's great to do it in such a stressful race, where it's so easy to make a mistake.
"The last few laps were a little bit stressful but what an amazing way to start the year.
"We have a lot of work to do in this car and if you relax, you have failed.
"In Formula One if you start to think everything is good and groovy that is when you get caught.
"But I do think we are the favourites. We are the team to beat. The car is flying and there will be tracks where we are even better."
The Brit's win meant that for the first time since May 2022 - incredibly 1029 days ago - Verstappen is not the championship leader.
Not that Norris is getting too carried away as he added: "It doesn’t mean anything - I've not won it.
"I know what I'm capable of and I know what I can do. It's just round one...