Verstappen lost the lead from F1 title rival Lewis Hamilton at the start, but was able to get back in front after undercutting at the first round of pit stops, coming in at the end of lap 10.
Mercedes pitted Hamilton three laps later, and while he was able to close through the second stint thanks to his tyre advantage, Red Bull reacted first and brought Verstappen in for a second time on lap 29.
It left Verstappen with a 27-lap stint to complete to the finish, and he looked at risk of losing the win when Hamilton began to catch at a rate of one second per lap after making his final stop, cutting an eight-second gap down to less than two.
But after being instructed to look after his rear tyres so he could get a good exit out of the slower corners and into DRS zones, Verstappen managed to stabilise the gap, eventually crossing the line 1.3 seconds clear of Hamilton.
“We lost out at the start, so we had to try and do something else,” Verstappen explained in parc ferme after the race.
“But the tyre wear is quite high around this track, so we did go aggressive.
“I was not sure it was going to work, but yeah, the last few laps were fun. A bit sideways through the high speed corners, but super happy of course to hang on.”
The result means Verstappen now leads the drivers’ championship by 12 points with five races remaining, securing his first win at the Circuit of The Americas.
Hamilton had managed to briefly reduce the gap to less than one second in the closing stages, but never got close enough to use DRS and reel the Red Bull in.
“It was such a tough race,” Hamilton said. “[I] got a good start, gave it absolutely everything but at the end of the day they just had the upper hand this weekend.
“We couldn’t really ask for more, but a big, big thank you to my team for great pitstops, great hard work throughout the weekend.”
Red Bull team principal Christian Horner praised Verstappen for an “unbelievable” and “classy” victory, and admitted on Sky Sports after the race he was unsure the Dutchman could have held on.
“I really didn’t think he was going to pull that off,” Horner said.
“Lewis [had] eight lap newer tyres, the first set of hards that came off, we were pretty much down to the canvas, and we were thinking we wouldn’t have much at the end left.
“Lewis, you know the end of the race, he’s so strong and he’s gone long, he’s bought himself and advantage.
“To lose a race in the last couple of laps would have been really painful. Max just held on, he did a brilliant job and had just enough at the end there.”