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.
"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."
Source: Autosport