The Red Bull youngster, who only turned 20 at the end of September, celebrated his birthday with victory at the Malaysia GP a week ago.
But it was Hamilton - by Formula 1's increasingly young standards, something of an elder statesman on the grid at the age of 32 - who prevailed this Sunday at Suzuka as he fought off Verstappen for a win which propelled the Mercedes driver 59 points clear in the Drivers' World Championship.
Hamilton v Verstappen is something to savour. Hope that movie runs for a long time.— Martin Brundle (@MBrundleF1) October 8, 2017
In a light-hearted exchange during the post-race press conference, Hamilton said: "I was driving down the back straight at one point and I'm thinking 'Jeez, the guy behind me is so much younger than me, I've got make sure I kind of man up and show my age and make sure that I stay ahead. Show that I'm actually still very young at heart.'"
Sitting alongside Hamilton, Verstappen interjected: "I was thinking 'this guy's so old in front of me.'"
Hamilton responded: "Yeah, 'I'm not letting this little….'"
The joking aside, the mutual respect between Hamilton and Verstappen, considered to be F1's next superstar, runs deep and many in the paddock believe the pair could be team-mates at Mercedes as early as 2019.
"I am enjoying being in an era with such great young talent coming through," Hamilton said. "He'll be here far beyond after I stop. But until then, I will try and not give him too many poles or too many wins."
Mercedes and Ferrari are expected to launch a bidding war for Verstappen when he becomes available and the Dutchman reiterated this weekend that he is impatient to land a winning seat as quickly as possible.
"I just want to be in the fastest car," Verstappen told Sky F1. "I don't dislike [the idea of driving for Ferrari] at all.
"I just want to be in the fastest car in Formula 1 because that means you can win races and that's what I want to do."
Red Bull's attempts to retain both Verstappen and Daniel Ricciardo, a free agent at the end of next season, will be one of the running themes of 2018 with the team determined to retain a driver line-up wide recognised as the strongest in F1.
If either driver does depart then Carlos Sainz, on loan at Renault next year, will take their place.
"It is our intention to retain both of our drivers to until 2020," said Red Bull boss Christian Horner. "I wanted to keep Carlos under contract as an option should one of the drivers depart next year.
"But the absolute intention is we want Verstappen and Ricciardo in Red Bull. They both enjoy being in the team. The difference with Daniel is that for the first time in his career at Red Bull, he has actually got an end sight to his contract.
"As a dynamic between the two drivers, the youth and experience, it works very well."
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Source : https://news.sky.com/story/old-guy-lewis-hamilton-shows-age-no-barrier-to-beat-max-verstappen-11073482