Lewis Hamilton finished eighth in the opening practice session for the US Grand Prix.
Hamilton, who is set to wrap up his sixth world championship this weekend, used much of the running to trial next year's tyres.
But, in the closing moments, the Mercedes driver posted a lap good enough to finish inside the top 10.
Hamilton, boosted by the return of his regular race engineer Pete Bonnington, who was ruled out of last week's race in Mexico following a medical procedure, will be certain of clinching the title that takes him to within one of Michael Schumacher's record haul of seven if he finishes eighth here on Sunday.
The British driver, 34, has won on five of his last seven visits to the Circuit of the Americas, but his Mercedes team ran under the radar at an unseasonably cold Austin on Friday morning.
Hamilton finished 1.3 seconds down on Verstappen, while team-mate Valtteri Bottas, the only man who can stop Hamilton from securing this year's title, ended the running down in 17th.
Bottas, who must win to stand any chance of taking the title fight on to Brazil in a fortnight's time, also practised on next year's rubber with Mercedes turning one eye to 2019 and securing a seventh consecutive constructors' crown.
Verstappen could have won in Mexico last time out, but was stripped of pole and then collided with Bottas on the opening lap. Here, he led the way to suggest that Red Bull could be in contention once more.
Vettel finished 0.169 sec behind Verstappen with Albon nearly three tenths adrift of his Red Bull team-mate.
Pierre Gasly finished fourth for Toro Rosso ahead of Renault's Daniel Ricciardo. Ferrari driver Charles Leclerc was seventh.