The 32-year-old Briton, who started from a record 72nd pole position, recovered after losing his advantage at the start to regain the lead and steer his Mercedes to his ninth win this year, his fifth in Texas and the 62nd of his career.
With three races remaining, Hamilton leads Vettel by 66 points and can take the championship by winning, or finishing in the top five, at next weekend's Mexican Grand Prix.
"That was one of the fun races I've had in a while," said Hamilton. "But I was expecting it to be more of a tough fight with Sebastian.
"Maybe it will come next weekend in Mexico. I didn't get away to a great start. Seb got a great start, but I was chilled about it as I know you can overtake here.
"So I stayed cool and then it was great having that battle, trying to keep up, stay close, get within DRS.
"For me, it was very reminiscent of 2012 here, seeing Seb up ahead and wanting to have that real battle. That is what I looked for and that is what I enjoyed the most.
"But as I said, I was a bit surprised Seb didn't defend more, but it was still fair."
Hamilton added that he was delighted to play his part in the Mercedes team's victory in the constructors' championship for a fourth consecutive season.
"I want to say a big congrats to everyone in the team and everyone back at the factory," said Hamilton.
"There has been an incredible push for this kind of performance this year and we have really pulled together more than I have experienced and seen over the last five years to really get something quite special.
"Especially, to go from one car -- and one set of rules -- to another, which has never been done and I am proud to be a part of it."
Vettel, now 66 points behind Hamilton with only 75 remaining, said: "At the start it was looking good. We got past Lewis, but then we realised we could not match his pace today.
"Towards the end, we decided to pit again so the last laps were especially exciting, but overall it was not the result we wanted."
Hamilton revelled in his podium interview with multiple Olympic sprint champion Usain Bolt, who he had taken as a passenger for a few laps of the Circuit of the Americas before the race
"I'm still feeling nervous," said the Jamaican runner. "That was a fantastic experience.
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