Verstappen holds off Hamilton to win US Grand Prix thriller
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Verstappen, in a Red Bull, claimed his first victory at the Circuit of the Americas in front of 140,000 fans.
Mercedes star Hamilton, the reigning world champion, had cut the deficit in the race to under a second on the penultimate lap but could not find a way through the Dutchman's impressive defence.
"Of course we lost out in the start so we had to try and do something else," said Verstappen.
"The tyre wear is quite high around this track, we went aggressive and I was not sure it was going to work but the last few laps were fun.
"A bit sideways through the high-speed corners but super happy to hang on."
Sergio Perez completed the podium for Red Bull ahead of Charles Leclerc in a Ferrari and McLaren's Daniel Ricciardo.
"I think I've aged about 25 years in that race," said Red Bull boss Christian Horner. "I really didn't think we were going to hang on."
Hamilton admitted Red Bull were stronger.
"Max did a great job today," he said on the podium.
"It was such a tough race. I got a good start, gave it absolutely everything but at the end of the day, they just had the upper hand this weekend and we couldn't really have asked for more."
Hamilton, second on the grid, stunned pole-sitter Vertsappen at the start.
The Briton edged ahead at the first turn and stayed in front for 10 laps until Red Bull pulled off what they hoped would be a tactical coup.
'Sliding a lot'
"He's sliding a lot and I have a lot more pace," Verstappen told his team over the radio.
By calling in the Dutchman, who had a sluggish Hamilton in his sights, for an early pit stop, he was able to under-cut the champion.
"We pulled the trigger early, but Max is doing a good job," Horner told Sky Sports from the pit wall.
"It's like a game of chess this race."
Hamilton consistently chipped away at the lead and by half-distance in the 56-lap race, he had slashed the deficit to 3.3 seconds.
His efforts were further aided by a virtual safety car period called so marshals could collect some debris off the track.
When he returned, Perez conceded track position to allow the Dutch driver to slip into second spot, albeit more than 16 seconds back from the seven-time champion.
"This race is all going to be about the last five laps so we'll see how it pans out," Horner said.
"The pace was just starting to drop off and with three seconds behind there was a chance for an undercut."
Behind Perez, as the race entered the last 20 laps, Leclerc and Mercedes' Valtteri Bottas were scrapping over fourth place.
At the back, Pierre Gasly, who had started on the fourth row, was forced to retire when the suspension failed on his AlphaTauri.
Both Alpines of Fernando Alonso and Esteban Ocon were also soon forced into an early finish.
The British driver ate away at the advantage, aided by Verstappen running into a wall of backmarkers.
With 10 laps left, the gap was down to 2.3sec while Perez was a distant third almost 30 seconds off the lead.
However, Verstappen held on under intense pressure over the last two laps to secure a crucial victory.