Hamilton, who needed to finish only seventh at the Autodromo Hermanos Rodriguez to beat Sebastian Vettel to the title with two rounds to spare, spent much of the race at odds with his Mercedes team as he struggled for pace.
Hamilton won his fourth title in Mexico a year ago after starting third and then having to fight back from last to ninth following an opening lap collision with Vettel, who had been on pole but lost out to Verstappen.
I really don't know what happened. Ferrari's Vettel finished second.
But the Dutch driver was able to start the race off strong, passing Ricciardo in the run down towards Turn 1 and controlled the race, pulling away from Lewis Hamilton to his fifth victory in F1.
"He drove superb all year".
Hamilton started a trend with Ricciardo and Verstappen following suit on laps 12 and 13.
"I knew the pace was in the auto - Max showed that all weekend - I just knew it was putting together a clean lap at the end".
"This car's cursed", Ricciardo said. He almost found it when he saw a gap between the Red Bulls and tried to take it.
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The top-seeded Swiss seemed in control after winning seven straight games to take the first set and lead by a break in the second. After struggling in the second set, Copil recovered and finished the match off with 10 aces in the final set.
It goes without saying that Hamilton's championship charge has been aided by Sebastian Vettel's implosion, and, at the last count, the Ferrari driver's nine significant mistakes this year. "A party tonight? No, I'm going home!"
Ricciardo qualified on pole for Sunday's race in Mexico, but the Aussie could only manage 61 laps before yet another reliability issue forced him to retire for the eighth time this season.
Verstappen went on to dominate for the second successive year in Mexico while Ricciardo moved into second place by running a one-stop strategy.
Quite a drastic turn of fortunes for the two Red Bull drivers.
The world championship leader, who is within five points of clinching his fifth world title, struggled with tyre-wear and lack of mechanical grip with his Mercedes vehicle as he and team-mate Valtteri Bottas were outpaced.
"The whole qualifying was crap", he lamented "Again, same [engine] problems we had in practice two - engine braking not like I want to, rear locking the vehicle". In my mind it is just another day of fighting and I have more races to win, it is not over.
But Verstappen, 21, finished just 0.254 seconds clear of Hamilton, with Mercedes having taken a step forward overnight.
"We tried to make the best of it and I thought it was going to be enough for pole with the problems we had".
Nico Hulkenberg was sixth for Renault ahead of Charles Leclerc of Sauber, Stoffel Vandoorne of McLaren, Marcus Ericsson in the second Sauber and Pierre Gasly of Toro Rosso.