Hamilton, who started from pole position, led virtually every lap in Austin to record his 50th career win 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 yesterday he 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.
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.
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.
In a race of little incident, Sebastian Vettel finished fourth while Fernando Alonso fought his way past his compatriot Carlos Sainz on the penultimate lap to take fifth. 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.