The Briton, last year's pole-sitter in Austin and 22 points adrift of the Australian with six rounds remaining, lapped the Circuit of the Americas with a best time of one minute 33.294 seconds.
Sauber's Nico Hulkenberg was second fastest, 0.255 slower, with Piastri 0.279 off Norris' pace.
Aston Martin's Fernando Alonso was fourth on the timesheets, 0.345 slower, with Red Bull's Max Verstappen fifth and 0.354 off Norris' time.
The weekend is being run to the sprint format for the fourth time this season, meaning the Friday slot usually taken by second practice is instead a qualifying session for the Saturday 100km race.
The session was halted briefly to clear debris at the penultimate corner, with something shed from Lance Stroll's Aston Martin.
Williams' Alex Albon was sixth with George Russell, winner of the previous race in Singapore for Mercedes, seventh and Ferrari's Lewis Hamilton eighth.
