The reigning two-time champion relegated championship leader and Mercedes teammate Nico Rosberg to second place at the Circuit of Americas in Austin, Texas.
It has cut the gap between the pair to 26 points, with three rounds remaining of the 2016 season.
"Perfect race, Lewis," came the message from his team after an imperious and untroubled drive.
It was certainly a 'must-win' for Hamilton, who charged into the lead from the front of the grid as Red Bull's Daniel Ricciardo forced his way past Rosberg into second place.
Germany's Rosberg managed to get past Ricciardo during a Virtual Safety Car period, ironically put in place after Ricciardo's teenage teammate Max Verstappen had to stop on the track with a technical issue.
"Second place is ok, it was damage limitation," admitted Rosberg.
Australia's Ricciardo eventually finished third, with Sebastian Vettel in fourth for Ferrari, who lost Kimi Raikkonen to a retirement.
Two-time champion Fernando Alonso was a fine fifth for McLaren, with Carlos Sainz in sixth for Toro Rosso.
It was Hamilton's first victory since the German GP at the end of July, his challenge compromised by engine issues and the consistent performances of Rosberg, who is seeking his first world title.
Even with victory in the remaining races, culminating in the finale in Abu Dhabi at the end of November, Hamilton's fate remains out of his hands as Rosberg can come out on top with second places in all three.
"All I can do is my best, Nico has been driving fantastically well, so the battle will continue, I will be going for it," he said.
It was his seventh win of the season and 50th of his glittering career, which has seen him win three world titles, the last two with the dominant Mercedes outfit.
Texas also remains a happy hunting ground for the Briton, who clinched the title there last season and was winning for the fourth time on the circuit.
His popularity has helped fuel interest in F1 in the United States, with sporting celebrities skier Lindsey Vonn and tennis superstar Venus Williams among a massive crowd watching the 56-lap race, while Taylor Swift provided the pre-race entertainment.
The F1 circus now moves onto the Mexico for next weekend's race, with the title race still very much alive.