He took advantage of a safety car to pit from the lead and emerge ahead of Max Verstappen, who had boxed just laps earlier.
The McLaren ace then weathered a short attack from the Dutchman before pulling a 7.6 second gap by the time he took the chequered flag for his maiden F1 victory.
But it was the other Red Bull driver with whom Norris had the closest scrape with during the race.
Norris' start hampered by Perez move
Norris started from P5, one position behind Perez and a spot ahead of Australian teammate Oscar Piastri.
The Mexican got an ideal launch when the lights went out and sent a bold lunge down the inside of both Ferraris.
As he did so, he locked his front-right tyre and almost careered into team-mate Verstappen and forced Norris to take evasive action when rejoining the track.
Norris recovered from that scare to eventually win the race, but criticised Perez's move on reflection.
"It was a tricky first stint, I was stuck behind Perez," he told the BBC's F1: Chequered Flag podcast. "I had to get out of Perez’s way in Turn 1 because he freaking came in like a rocket!
“So I stayed in the race; that’s a good start. Just from that point on I was like, ‘Ok, it’s a long game, there's not going to be a lot of overtaking, it's going to be a race about tyre management and strategy'.
“Everyone knows that the longer you can go, the more opportunity you buy yourself with safety cars and VSCs and all of those things.
“Today was my day! Today was the day when someone was like, ‘I'm gonna throw a safety car now’, and it all worked out perfectly.
"Whoever that person was, I thank them, and I share my trophy and champagne with them!”