Hamilton, who started from pole position, led virtually every lap here in Austin to record his 50th career victory and move to within 26 points of 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.
Despite Hamilton claiming his first win since July’s German Grand Prix, the championship battle remains firmly in Rosberg’s hands with only three rounds remaining.
Hamilton’s championship defence has been plagued by mechanical woes and slow starts, but perhaps, inspired by the presence of astronaut Tim Peake here on Sunday, the Briton got the perfect lift-off.
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. Hamilton, who spends much of his free time in America, has now won across the pond on an impressive five occasions.
While it was a Sunday cruise for Hamilton, the same could not be said for Rosberg 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 after suffering a terminal engine failure.
With his Red Bull adjudged to be in a dangerous position on the race track, the virtual safety car was deployed to slow down the field. Both leader Hamilton, and his Mercedes team-mate Rosberg, dived into the pits for a set of new tyres, and Rosberg emerged ahead of Ricciardo much to the Australian’s frustration.
“So they got a free pit-stop basically?” Ricciardo asked his Red Bull pit wall.
“Yes mate, that is correct,” came the response. “That is so f*****,” Ricciardo replied.
With Ricciardo now out of the way, Rosberg lay in second, but the German was unable to do anything about the gap to his dominant team-mate.
Indeed Hamilton crossed the line nearly five seconds clear of Rosberg, lapping the entire field up to seventh.
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 fought his way past his compatriot Carlos Sainz on the penultimate lap to take fifth. “Yee-haw,” the McLaren driver yelled after he made his move.
Felipe Massa finished in seventh for Williams.
Jenson Button, who made up an impressive nine places on the opening lap after starting a lowly 19th, finished in the points in ninth. British rookie Jolyon Palmer crossed the line in 13th.