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Verstappen finished second with Valtteri Bottas third for Mercedes after a controversial, roller-coaster weekend in Brazil.
Seven-time world champion Hamilton was second for Mercedes, holding off Red Bull's Sergio Perez who became the first Mexican to stand on his home podium.
The win was Verstappen's eighth of the season, and first in America, but one he had to sweat for in front of a sell-out 140,000 crowd.
The 24-year-old Red Bull racer also gave the seven-time world champion, the most successful driver of all time, a single digit salute as the Mercedes accelerated away on a hot and humid Texas afternoon at Austin's Circuit of the Americas.
Red Bull's Max Verstappen finished second to take back the Formula One world championship lead.
Seven-time world champion Hamilton is now two points clear of Verstappen with seven races remaining.
Formula One title rivals Lewis Hamilton and Max Verstappen collided and crashed out of the Italian Grand Prix at Monza on Sunday.
The disqualification meant Mercedes' seven-time world champion Hamilton inherited the position and gained two extra points in his battle with Red Bull rival Max Verstappen
The new deal covers 2022 and 2023.
The 23-year-old, now level with Hamilton on three wins for the season, also set the fastest lap and has 131 points to Hamilton's 119.