The McLaren driver had endured a dismal qualifying in Mexico City after making a mistake on his only run in Q1 and failing to make it through, ending up 17th on the grid.
But after trying an alternative strategy early on in the grand prix with the softs, he made good progress to get up to 10th before the mid-race red flag that helped reset any tyre offset against rivals.
However, in backing off to avoid a crash at the restart, Norris tumbled down the order to 15th before staging a brilliant recovery to charge through and take fifth.
Speaking to Sky after the race, Norris said that his feat was made even more impressive by the fact that he had to battle and overtake some tough rivals, including George Russell and Daniel Ricciardo.
"It's very special," said Norris. "It wasn't from 20th to 10th. It was from 14th to fifth. It was against George and Alex [Albon] and Oscar [Piastri] and Daniel. So, it was against some quick guys and smart guys.
"But I played it all well, I played the overtakes well, I put them into awkward positions, and I managed to get past them all very quickly, which allowed me to end up in P5."
He added: "My main thing was just staying out of trouble. And it all paid off. So, it's enjoyable racing like this, and I wish I could be a little bit further up. I think we could have challenged for some silverware."
Asked which was the overtake that he enjoyed the most, Norris said: "Probably the one on Daniel...he's the late braker!
"We must have been very, very close. I braked earlier than I think he thought I would. So, then he braked and I just got off the brake and got him on the outside.
"Whenever you're doing these overtakes, and having to prepare exits and all of it, you enjoy the whole thing, so I don't really mind who it is. It's just they're all good."
Restart woes
Norris said the poor restart that nearly derailed his afternoon was triggered by him not being able to get his tyres into the right operating window.
"The restart is tough," he said. "We just didn't get it right. My first start was good, but the second one not so good.
"I think we struggled a little bit too much with the power unit temperatures and things like that, so I couldn't get the tyres and things in the correct window for the restart.
"I paid the price a little bit. I then had to avoid some incident, and I had to back out quite a bit down the straight, which could have gone a lot worse.
"But after that, I just stayed calm and got the tyres in a good window and went from there. It was enjoyable, I didn't think I'd get back to P5. So encouraging pace from the car."
