Hamilton, who wants to see out the title which will draw him level with Juan Manuel Fangio on five world championships with a victory, is in striking range of the Red Bulls but, crucially, ahead of his sole rival.
The Mercedes star had just secured his fifth championship, becoming only the third driver in Formula One history to do so, yet this triumph in the thin air of Mexico City didn't possess the drama of his first title in 2008, or the relief of beating his bitter foe, Nico Rosberg at the season-decider in Abu Dhabi six years later.
Hamilton performed a series of celebratory doughnuts for the 40,000-strong crowd in the former baseball stadium section of this unique Autodromo Hermanos Rodriguez venue, before standing on top of his auto to salute them.
After failing to wrap up the title the previous weekend in the United States Hamilton turned up at the Autodromo Hermanos Rodriguez with Vettel needing a victory, with the Briton outside the top seven to prolong the title race.
Anthony acted as his son's manager before their acrimonious split in 2010.
"It's a very odd feeling right now", Hamilton said as he got out of his vehicle and celebrated.
"I can't be too hard on myself what I did in Germany". It is a very humbling experience.
"To complete this when Fangio did it with Mercedes is an incredible feeling and very surreal".
After taking pole, Ricciardo had a poor start and was pushed down to third by Verstappen and Hamilton.
The unlucky Ricciardo later suffered another retirement in a year blighted by bad luck, allowing Hamilton to reclaim the place, with his teammate Valtteri Bottas in fifth.More news: President Trump blasts Paul Ryan over birthright citizenship comment
As they roared down to Turn 1, Hamilton then locked up his front-left tyre, and in a plume of white smoke, ran on to the grass. The 110,000 spectators groaned and roared in equal measure.
Hamilton prepared for the floodlit Marina Bay street circuit test by launching his new fashion label in Shanghai and NY, but the frantic time-zone hopping schedule only served to energise the unstoppable Briton. "These tyres are dead", he yelled. He would re-join in fifth.
From there, Hamilton just made sure he got his vehicle over the line, and was promoted one place after Ricciardo's engine blew up with 10 laps remaining.
"It was a disgusting race", Hamilton conceded in his post-race interview.
"I'm holding a lot in". "I'm not superstitious or any of that bulls***t, but the car's cursed".
"For Lewis now, with five titles, unbelievable", said 2016 world champion Rosberg, in a message of congratulations he posted on his YouTube channel after the race.
"Obivously not an easy day", said Vettel.
Vettel took pole and dominated right up until a safety vehicle seemed to put victory in Valtteri Bottas' hands with Hamilton set for no better than third.
"It is a disgusting moment for me".
"I've had three times now in my life that sort of disappointment, where you realise that you can't win the championship any more and those are not happy days".