Hamilton only needed to finish eighth to guarantee a third crown on the bounce, but fought his team-mate, and only remaining title rival, all the way to the end at the Circuit of the Americas.
Pole-sitting Bottas took the victory he required to keep his flickering hopes alive, but Hamilton joining him on the podium extinguished them, with the Brit holding off Max Verstappen for second.
Hamilton leaves Juan Manuel Fangio behind on the all-time list of F1 world champions, with only Michael Schumacher ahead on seven titles.
That and many other records set by the German maestro are in Hamilton’s sights, but he just fell short of nudging closer to Schumacher’s record of 91 race wins.
Hamilton started fifth, but the equation was made much more comfortable amid a wretched start to the race for Ferrari, which saw both Charles Leclerc and Sebastian Vettel drop back before the German suffered a dramatic suspension failure on lap eight and retired.
But Hamilton was not taking it easy, committing to a one-stop strategy as Bottas and Verstappen battled over two stops.
Bottas had enough in the tank to pass his team-mate with four laps to go, securing his fourth win of the season.
But Hamilton would not be denied, securing the title with a podium finish for the first time since 2015, when victory at this same venue did the job for title number three.