"I wanted it more," said Hamilton. "I was hungrier than him. It's not even possible he wanted it as much as me."
'One of the best wins' for Hamilton
Vettel responded: "I don't know about that. It was very close between us."
The result means the race for the title goes down to the final race in Brazil this weekend, with Vettel, champion for the last two years, holding a 13-point lead over Ferrari's Fernando Alonso, who was world champion in 2005 and 2006.
Victory for Alonso at Interlagos would give him his third drivers' crown if Vettel finishes lower than fourth.
Second place for the Spaniard would mean he would only win the title if Vettel failed to make the top seven. Third spot for Alonso would require Vettel to finish lower than ninth.
It was an impressive drive from Hamilton, who leaves McLaren at the end of the season to join Mercedes.
He then set off in pursuit of Vettel and finally overtook his rival after 38 laps of pressure and a little help from the HRT of Narain Karthikeyan, who slowed the German as he was being lapped.
"It was actually quite tricky," said Hamilton. "I seemed to be catching him in the first sector but then, coming out of Turn 9, he'd get a gap and it was difficult to be close enough for the back straight.
"How many times has it happened to me when I've been caught out by backmarkers? It finally worked in my favour for once.
"I knew it was going to be that lap, so I turned the engine up to maximum revs, went to go on the outside but he closed the door, went to go to the inside, but he started to move back. I was very lucky, it was very close, and I managed to pull off the pass."
Vettel added: "I think we did a good job keeping him behind for most of the race. Unfortunately, I had a little but of traffic which allowed him to be close and gave him a chance for free - and he took it. There wasn't much between us."
In achieving victory, Hamilton became only the second driver to win the United States Grand Prix in two separate locations. The Briton
also won in Indianapolis in 2007.
emulating Formula 1 legend Ayrton Senna, who won the race in Phoenix and Detroit.
Alonso must finish on the podium to stand a chance of snatching the title from Vettel
Victory for Alonso would give him the title if Vettel finishes lower than fourth
Second place for the Spaniard would mean he would only win the title if Vettel failed to make the top seven
Third spot for Alonso would require Vettel to finish lower than ninth
"It was wicked, I loved it so much," added Hamilton. "I'm so happy. I nearly lost my voice when I came across the line. For that whole in lap, I was screaming all the time, I was so happy. Not cool at all.
"We really deserved this one. Sebastian put up a great fight. The Bulls have been incredibly dominant for some time so to be able to topple them is a wicked feeling."
Hamilton admitted the team's recent reliability issues played on his mind in the closing laps.
"I just rubbed the car," he said. "I was like: 'Come on baby, we can make it.' To finish on a high is really special and hopefully we can go to Brazil with similar pace."
McLaren team boss Martin Whitmarsh added: "Lewis did a fantastic job. Sebastian is a quick driver but you can put him under pressure and you can race him. He did that fantastically.
"He closed in and he was patient, but just got by brilliantly. He had to overtake Mark along the way as well, so overtaking both Red Bulls today is a nice feeling.
"With one race to go, we'd like to win that as well. That would be some compensation for some of the disappointments, some of the failures, that we've had this year.
"We've got to get better, we've got to get stronger, we've got to make less mistakes. We'll learn from that and come out stronger next year, but at the moment we've focused now on Brazil."
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