Hamilton’s first win since the German Grand Prix in July puts him 26 points behind his Mercedes teammate with 75 available in the remaining three races.
Rosberg finished second after recovering a position lost to Red Bull ‘s Daniel Ricciardo at the start, and remains heavily tipped to win the championship.
The German was able to a “free stop” under a Virtual Safety Car deployed when Max Verstappen ‘s Red Bull broke down and the Dutchman, on orders from his team, opted to park alongside a wall.
This allowed Rosberg to retain second place, forcing a frustrated Ricciardo to settle for third ahead of Ferrari ‘s Sebastian Vettel.
Toro Rosso ‘s Carlos Sainz , meanwhile, claimed a career-best sixth despite being overtaken on the final lap by McLaren ‘s
Fernando Alonso , who faces a stewards’ investigation for banging wheels with Felipe Massa.
United States GP result:
1. Lewis Hamilton, Mercedes, 1:38:12.618
2. Nico Rosberg, Mercedes, + 4.520
3. Daniel Ricciardo, Red Bull, + 19.692
4. Sebastian Vettel, Ferrari, + 43.134
5. Fernando Alonso, McLaren, + 93.953
6. Carlos Sainz, Toro Rosso, + 96.124
7. Felipe Massa, Williams, + 1 lap
8. Sergio Perez, Force India, + 1 lap
9. Jenson Button, McLaren, + 1 lap
10. Romain Grosjean, Haas, + 1 lap
11. Kevin Magnussen, Renault, + 1 lap
12. Daniil Kvyat, Toro Rosso, + 1 lap
13. Jolyon Palmer, Renault, + 1 lap
14. Marcus Ericsson, Sauber, + 1 lap
15. Felipe Nasr, Sauber, + 1 lap
16. Valtteri Bottas, Williams, + 1 lap
17. Pascal Wehrlein, Manor, + 1 lap
18. Esteban Ocon, Manor, + 2 laps