Lewis Hamilton believes the championship battle is firmly back on after he turned in a commanding performance to win the United States Grand Prix and complete the first leg of what would be a remarkable fightback in the title race.

Hamilton led virtually every lap in Austin from pole to become only the third driver in Formula One history to record 50 career wins, and move to within 26 points of his Mercedes team-mate Nico Rosberg.

Rosberg spent much of the race behind Daniel Ricciardo, but finished in second place after he leapfrogged the Red Bull driver during his second pit stop.

But, despite Hamilton claiming his first win since July's German Grand Prix, the race for this year's title remains out of his control. Indeed, Rosberg could clinch the championship in Mexico next Sunday if he wins and Hamilton fails to score.

"All I can do is my best, and continue to drive like I have done this weekend," said Hamilton, who has now won in America on five occasions.

"Nico has been driving fantastically well all year and the battle will continue.

"I know we have all this support, so please keep your fingers crossed. I am going to be going for it."

Hamilton's victory in Austin saw the 31-year-old Briton join Michael Schumacher and Alain Prost in racking up a half-century of grand prix races. He is now just one victory shy of Prost in the all-time winners' list.

"I completely forgot that it was going to be the 50th win," Hamilton added. "It has been a long-time coming.

"I have been here for 10 years and I have had lots of ups and downs. It is very surreal - I can't believe there is only three of us - but hopefully now on to bigger and better things."

Hamilton's championship defence has been plagued by engine problems and slow starts, but, perhaps inspired by the presence of astronaut Tim Peake, the Briton got the perfect lift-off when the lights turned green on Sunday.

Hamilton blasted up to turn one, comfortably keeping Rosberg at bay, and from there he never looked back. Of his seven wins this season, none will have been more straightforward.

But while it was a Sunday cruise for Hamilton, the same could not be said for his Mercedes team-mate, who was passed by Ricciardo at turn one on the opening lap.

It remained that way until lap 31 when Ricciardo's Red Bull team-mate Max Verstappen was forced to park his car following a gearbox failure.

With his Red Bull adjudged to be in a dangerous position, the virtual safety car was deployed to slow down the field. Rosberg dived into the pits for a set of new tyres, and emerged ahead of a frustrated Ricciardo.

"I gave it everything to come back and second is okay," championship leader Rosberg said. "It was damage limitation today.

"I wanted to win in America, but it wasn't to be. I was going for it flat out all the way to the end."

In a race of little incident, Sebastian Vettel finished fourth, while his Ferrari team-mate Kimi Raikkonen retired after he was released from his third pit-stop with the wheel gun still attached.

Raikkonen was left stranded at the end of the uphill pit lane at the Circuit of the Americas before coolly free-wheeling his Ferrari back into the pits.

Fernando Alonso finished fifth, with McLaren team-mate Jenson Button in ninth.