As his title rival Sebastian Vettel struggled through a difficult second session in which he spun off in his Ferrari, Hamilton smashed the lap record at the Circuit of the Americas.
His best lap in one minute and 34.668 seconds saw him outpace nearest rival Max Verstappen, who earlier signed a new deal to stay at Red Bull until 2020, by nearly four-tenths of a second and four-time champion Vettel by half a second.
"It's been an interesting day with lots of ups and downs in terms of how the track has moved around and how the car feels," said Hamilton.
"It was amazing to have so much support -- which I am super grateful for. I'm excited to see everyone tomorrow."
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Hamilton, who has dismissed talk of clinching the world title this weekend as "silly", can take his fourth championship if he wins and Vettel fails to finish in the top five on Sunday.
Vettel, who has seen his championship challenge undermined by accidents and engine problems in the last three races, admitted that he had suffered from "a messy afternoon".
"We have to take it as it is right now and make sure that the car is in good shape to get the rhythm and then I think we should be quick.
"It's important to feel comfortable. Obviously, we're missing some laps, but I'm sure with a couple of successive laps tomorrow it should be better."
After failing to finish two of the last three races in Asia, Vettel may have been happy to emerge unscathed on Friday, but he completed only 11 laps compared to Hamilton's 26 laps in the second session.
Two-time champion Fernando Alonso was seventh fastest ahead of Felipe Massa of Williams and the two Force India cars of Sergio Perez and Esteban Ocon.
Debutant Brendon Hartley, the first New Zealander to race in Formula One for 33 years, was 17th on his first run with Toro Rosso, but is expected to start Sunday's race from the back of the grid after taking a penalty for having a new engine.