A slender one point is the gap between the teammates and title rivals with four races to go.
Max Verstappen, who finished third, remains in the hunt for a fifth successive title with Red Bull, 36 points behind Norris.
"This is awesome and unbelievable here, my first win here in Mexico and a beautiful one to win especially here in the stadium," said Norris.
"A pretty straightforward race for me which is just what I was after. A good start, a good launch and a good first lap, and I could go from there," added the Briton.
Ferrari's Charles Leclerc took second, albeit over half a minute behind the impressive Norris who with this potentially pivotal win has set up a gripping run in to the season-closer in Abu Dhabi in December.
Haas rookie Oliver Bearman achieved his best career result in fourth at a baking hot Autodromo Hermanos Rodriguez circuit.
Piastri finished fifth to set up a gripping end to the season with four races to go.
