Hamilton's first win since the German Grand Prix in July puts him 26 points behind Rosberg with 75 available in the remaining three races.
Lewis Hamilton celebrated his 50th Formula One victory on Sunday with a pole-to-flag U.S. Grand Prix drive that kept his title hopes alive and trimmed Mercedes team mate Nico Rosberg's lead to 26 points with three races remaining.
Rosberg, who had been chasing his 10th triumph of the season, finished second on a sunny Texan afternoon with a big crowd but little drama -- even if Hamilton spent much of it worrying about reliability.
The straightforward victory was Hamilton's fourth in Texas in five seasons and ended a barren stretch for the triple world champion dating back to his last win in Germany in July.
"This has always been a good hunting ground for me," said the Briton, the third driver after Michael Schumacher and Alain Prost to win 50 races, in a podium interview conducted by British actor Gerard Butler.
"I love being here in the States, it very much feels like home," he added, with tennis player Venus Williams and skier Lindsey Vonn watching on.
"All I can do is do my best and continue to drive as I have this weekend," said Hamilton, who confessed he had completely forgotten that it would be his 50th win. "Nico has been driving fantastically well all year so the battle will continue."
Rosberg, finished 4.5 seconds behind and had dropped back to third at the start before events lent the German a helping hand.
Australian Daniel Ricciardo, who had seized second at the start, was third for Red Bull but his Dutch team mate Max Verstappen failed to finish due to a gearbox failure.
Rosberg, whose advantage means he can still take his first title without having to win again this season, said it was 'damage limitation'.
The German has 331 points to Hamilton's 305, with seven points the difference between a win and second place.
The Mercedes drivers are the only ones in title contention and the team has already won the constructors' championship for a third year in a row.
Hamilton, who won his third title at the circuit last year after a Rosberg error gifted him the race win, shook hands with his team mate as they waited to go on the podium.
The body language contrasted to the 2015 aftermath, when Hamilton tossed Rosberg a cap and had it thrown back at him.
Verstappen had pushed Rosberg hard early on but any hope of getting between the Mercedes drivers ended when he pitted with his team not expecting it.
The 18-year-old then dropped to a crawling pace before pulling across the gravel and parking up but marshals were unable to move the Red Bull to safety without the use of a crane, leading to a virtual safety car.
That allowed the Mercedes drivers to pit and gain time on Ricciardo, who had already done so. "They basically got a free pit stop," said the exasperated Australian over the radio.
Verstappen said the team had told him to keep going initially.
Ferrari's Sebastian Vettel finished fourth but a bungled stop put paid to team mate Kimi Raikkonen's race with the Finn leaving before the wheel had been fully detached.
"I saw some sparks coming out. At the end of the pitlane the team told me to stop ... the rear wheel nut had not fitted properly," said Raikkonen, who let the Ferrari roll back before parking up.
Ferrari were fined 5,000 euros ($5,439.00) for the unsafe release.
Fernando Alonso was fifth for McLaren with fellow-Spaniard Carlos Sainz sixth for Toro Rosso and Brazilian Felipe Massa seventh for Williams.
Mexican Sergio Perez finished eighth for Force India, after fighting back from the rear following a first lap tangle with Toro Rosso's Daniil Kvyat, and McLaren's Jenson Button was ninth.
Kvyat collected a 10 second time penalty for causing the collision.
Frenchman Romain Grosjean collected a point for Haas, the first U.S.-owned team in 30 years who were making their home debut, but Mexican team mate Esteban Gutierrez failed to finish.