Sargeant was classified 10th at Austin's Circuit of the Americas after Mercedes' Hamilton was stripped of second place and Ferrari's Leclerc lost his sixth place when their cars failed post-race checks.
The last U.S. driver before the Florida native to score in a grand prix was Michael Andretti with McLaren in 1993.
"It’s amazing to score my first point in F1 on home turf after the challenging weekend I’ve had," said Sargeant, who failed to finish the previous race in Qatar after suffering exhaustion in the heat.
"I’m so proud of this team and myself for the hard work and progress we’ve been making this season," added the rookie whose seat for next season is far from certain.
"We worked hard overnight to find a direction with the car that was going to be positive, and we found that... The pace was so much better today, and I was driving really well."
Williams also had Alex Albon finish in ninth place, with the team having two drivers in the top 10 for the first time since the 2021 Hungarian Grand Prix.
The team are seventh out of 10 in the constructors' standings, 10 points clear of eighth-placed Alfa Romeo with four races remaining.
Australian Daniel Ricciardo, returning from injury at AlphaTauri, is now the only driver on the starting grid yet to score this season.
