The Dutchman, who will make his 100th Grand Prix start on Sunday, clocked a best lap in one minute and 34.057 seconds to outpace the four-time champion German by 0.169 seconds.
Verstappen had pole position taken from him in Mexico where he was penalised retrospectively for ignoring yellow flags before collecting a puncture in the race, falling to the back of the field and then finishing sixth.
Five-time champion Lewis Hamilton, who is poised to clinch his sixth drivers' title, spent most of the session working on his Mercedes' set-up permutations.
Many of the drivers were lapping on the 2020 test tyres, supplied by Pirelli, on what was an unexpectedly chilly morning at the Circuit of the Americas where many team members chose to wear woolly hats for extra warmth and drivers' grumbled about the surface of the circuit.
"These bumps are insane out here," said champion-elect Hamilton. "I don't know if this track is safe."
Hamilton needs only four points, achieved by finishing in the top eight, on Sunday to ensure he is champion again while teammate Valtteri Bottas can only stop him claiming a sixth crown by winning the race and hoping his team-mate fails to score the points.
Hamilton briefly jumped up to fourth behind Alex Albon, in the second Red Bull, and then had his lap deleted for running wide, like many others, at Turn 19.
In the final seconds, he clocked another fast lap to take eighth, but without threatening the top positions.
This left Pierre Gasly in fourth for Toro Rosso ahead of Renault's Daniel Ricciardo, Romain Grosjean of Haas, Charles Leclerc in the second Ferrari, Hamilton and Lance Stroll of Racing Point.
Kevin Magnussen was 10th in the second Haas with Bottas, who did little running, down in 17th in the second Mercedes.