Norris finished second in Shanghai after benefitting from a safety car period to make his only pitstop and come out ahead of Sergio Perez, but then managed to keep his hard tyres alive to comfortably control the gap with the Mexican.
The result came as a surprise for McLaren at one of its intrinsically worst circuits, for while it could keep up appearances with strong qualifying performances, it struggled with tyre degradation in Saturday morning's sprint race.
Norris started the sprint on pole, but after slipping up at the start he fell back to sixth, ahead of team-mate Oscar Piastri and behind both Ferraris.
Those struggles made him bet with race engineer Will Joseph that he would fall back as far as 35 seconds behind Charles Leclerc and Carlos Sainz. Instead he finished 10 and 20 seconds ahead, respectively.
"I made a bet to how far behind the Ferraris we would finish today and I thought 35 seconds and I was very wrong by that," Norris laughed, after trailing winner Max Verstappen by 13 seconds for his 15th career podium.
"I'm happy to be wrong with myself and my own bets. I'm happy for the whole team, they deserved it.
"Today just worked out, I don't know why. I really wasn't expecting it to be the kind of race we had today.
"But I got comfortable, could manage the tyres a lot, which was a much easier task than what I had yesterday. And I could just push, the car felt great and felt comfortable."
Norris said he was surprised by Ferrari's relative lack of performance in China as well as his ability to split the two Red Bulls, which landed him the 'driver of the day' award from the fans.
"I was surprised by many things, the lack of pace from Ferrari today, our good pace comparing to the Red Bull, which was so surprising. So I just wasn't expecting today at all," he expanded.
"I got everything ready to go home early and not be on the podium, so it's a pleasant surprise.
"It shows the team have done a good job. We're working hard and it's paying off."
