In sizzling conditions, Red Bull's four-time world champion led from pole position to the chequered flag to come home 7.959 seconds clear of title-chasing Lando Norris, of McLaren, with Ferrari's Charles Leclerc finishing third, 4.041 seconds adrift.
Australian championship leader Oscar Piastri of McLaren finished fifth.
It was Verstappen's fourth win in Texas and seventh on American soil, his fifth this year and the 68th of his career.
It was also, for Verstappen, the fourth race in succession in which he had out-qualified and out-raced both McLarens.
Verstappen has reduced Piastri's 104-point advantage over him to 40 with five races remaining.
Seven-time champion Lewis Hamilton was fourth in the second Ferrari ahead of Piastri and Mercedes's George Russell.
Verstappen said: "It's been an unbelievable weekend for us. I knew it wouldn't be straightforward, and the pace between us was close. But my first stint did it for me.
"Now we have a chance to be there (in the title race) and we just have to keep delivering like that in all the weekends to the end of the season and see what happens.
"It's exciting. We just need to keep up the momentum."
Norris was relieved to snatch second place after spending most of the race pushing to overtake Leclerc.
"It took me long enough! It was a good battle with Charles; he fought hard. It was tough... But I'm happy to take second."
Verstappen now has 306 points in the title race in third place, leaving Piastri on top with 346 points and Norris on 332. McLaren have already won the constructors' title for the second consecutive year.
The 28-year-old Dutchman has now collected 119 points from a possible 135 over the last five Grand Prix weekends.
Norris passes Leclerc, heaps pressure on Piastri
On another day of searing heat in Texas, with temperatures of 30C and 44C on the track - making it a 'heat hazard' race - Verstappen made a clean start to lead up the hill into the opening sequence of turns with Leclerc, the only top 10 driver on softs, passing Norris for second.
Hamilton and Piastri also advanced to fourth and fifth after a poor start from Russell, all of them on mediums as Norris and Hamilton chased Leclerc in the opening laps. That battle gave Verstappen a clear run, and he was three seconds ahead by lap four.
Having won Saturday's sprint to trim Piastri's championship advantage to 55 points, the Dutchman was revelling in his form and the role of hunter as McLaren's supremacy evaporated.
By lap 10, Verstappen led Leclerc by 3.3 seconds with Norris third, 1.4 adrift and Hamilton fourth, 1.9 behind him. Piastri was fifth, 3.2 seconds back.
For McLaren, it was shaping up as a nightmare for team boss Zak Brown, who feared "that Max guy getting in the middle of our fun."
Leclerc's softs were failing by lap 15, and Norris attacked, but the Monegasque defended, and a frustrated Norris collected three warnings for exceeding track limits before he passed him on lap 21.
But after a flurry of pit-stops, Verstappen emerged six seconds clear of Leclerc with Norris, back down in third again.
What seemed to be a pedestrian contest came to life in the final six laps when Norris attacked Leclerc, who was struggling on his worn mediums, and, after several attempts, dived past him at Turn One on lap 52.
That helped Norris trim Piastri's championship lead to just 14 points.