The 27-year-old Briton, who started second on the grid alongside the defending champion, made the most of his superior outright speed on Sunday to pass Vettel on lap 42 and claim the 21st victory of his career.
For Vettel, it was a personal disappointment, but not enough to prevent his Red Bull team from winning the constructors title for the third successive season.
Fernando Alonso of Ferrari finished third after starting seventh on the grid – thanks to his team's pragmatic decision to break the gearbox seal on Felipe Massa's car – and his podium finish ensured that the title battle will go down to the wire at next weekend's Brazilian Grand Prix in Sao Paulo.
Vettel goes to Interlagos with a lead of 13 points, on 273 points compared to Alonso on 260. Hamilton, who leaves McLaren for Mercedes next year, was intent on delivering another win for the team before his departure and did so with elan as he seized his fourth win this year.
Amazingly, it was the first time F1's best three drivers of the current crop had shared a podium and, to mark the Texan location, all three wore Stetson cowboy hats as they celebrated.
Interviewed by the 1978 world champion, American Mario Andretti, Hamilton said: "First-time winner! I'm so happy. The fans were amazing, thank you. It was such a warm welcome and one of the best, if not the best, race of the year – especially for me and the team.
'Proud of my team'
"It's been a long time since we had a win. I'm so proud of the team and grateful for the support we've had."
Vettel said: "I did my first race, five years ago, in the United States. It's nice to come back for my 100th GP.
"I'm happy for the team – we won the constructors' championship, so thanks to all of you.
"Now we have another step to make in Brazil. In terms of the championship, it's looking a bit better after today."
Alonso, greeted by chants of 'Alonso, Alonso' from a raucous crowd that included many Mexicans and Latin Americans, said: "The circuit is fantastic and the fans were fantastic all weekend."
In front of a sellout crowd of 135 000 at the new Circuit of the Americas and under a solid blue sky, Vettel made a near-perfect start to pull clear from his 36th pole position and into the lead with Red Bull team-mate Webber advancing to second behind him.
Hamilton, starting second, struggled with lack of grip on the slippery side of the track and could not defend against Webber, but stayed third up the hill and into the sweeping left-hander turn one as the field hustled together in the pack.
Alonso, starting seventh thanks to Ferrari's strategic decision to break the seal on Massa's gearbox and take a five-place penalty for the Brazilian, had a clean start and went round the outside of turn one and into fourth, taking full advantage of a poor start by Raikkonen.
It was a thrilling vision as the cars stretched out and began to heat their tyres to optimim levels, but the focus was clearly at the front of the field where Vettel was unable to shake off his pursuers.
Webber, racing in third, had the task of defending Vettel's position, but his part in the race ended after 17 laps when he was forced to retire due to a grearbox failure. By lap 34, after a series of pit stops for tyre changes, Hamilton had closed to within two car lengths of Vettel.
This created a sequence of dramatic laps during which Hamilton tantalised Vettel and the crowd by setting up a passing move, using his power advantage and Drag Reduction System (DRS) on the back straight, but without executing it until lap 42 when, after being held up by a back marker, Vettel could not resist him and Hamilton dummied one way and then passed him on the outside.
Alonso, driving steadily and quickly, knew his podium position was enough to heep his title dream alive and, thanks to a superb drive from Massa, knew also that he had a Ferrari in fourth behind him to protect him in the closing laps. – Sapa-AFP