It marked Verstappen's first race win in the United States, with Red Bull's decision to pit early in Sunday's race paying off.
Mercedes told Hamilton it was "all about the final three laps" and, though the reigning world champion came close, he just did not have enough to overcome Verstappen, who takes a 12-point lead into the final five races.
Verstappen has now won eight races in 2021. Only in 2016, when Hamilton lost out to Nico Rosberg despite winning 10 grands prix, has a driver who has collected at least eight victories failed to win the championship.
Red Bull did not have it all their own way, with Hamilton coming from second on the grid to nip ahead of Verstappen with a brilliant start, but the Dutchman regained the lead and held his nerve.
"We lost some time at the start, so we had to try and do something else," Verstappen said. "The tyre wear is quite high around this track, so we had to go aggressive but I wasn't sure if it was going to work.
"The last few laps were fun. A bit sideways through the high-speed corners, but super happy to hang on."
Hamilton was left frustrated by Mercedes' decision to pit late during the Turkish Grand Prix two weeks ago, but on this occasion, the Briton – who has won a record six times in the United States – had no such complaints.
"Congratulations to Max, he did such a good job today," Hamilton said. "It was such a tough race, had a good start, gave it absolutely everything but at the end of the day [Red Bull] just had the upper hand this weekend.
"I couldn't have asked for more, a big thank you to my team for great pit stops, great work throughout the weekend."
Both Verstappen and Hamilton also hailed the 140,000-strong crowd at the Circuit of the Americas, with F1® returning to Austin for the first time since 2019 due to the coronavirus pandemic.
"What an amazing crowd, to perform in front of you guys is such an honour," Hamilton added. "I think this is definitely our acceptance into the US.
"What a place to be, I hope we have more races out here, hope the sport continues to grow because you can see how great the fans are."
Verstappen echoed the sentiment, saying: "[The fans] have been incredible. It's amazing to be here and to see so many of you around the track."
Red Bull had a great day all-round, with Sergio Perez coming in third to seal the team's 200th F1® podium.
Perez's efforts were made even more outstanding by the fact the water system in the Mexican's car had a malfunction, leaving him unable to take on any fluid in scorching track conditions in Texas.
"Struggled massively. You know, since lap one, I ran out of water. I couldn't drink at all," he said.
"I think by the middle of my second stint it was starting to get pretty difficult, you know, losing strength. I think my toughest race ever, physically."