Hamilton on top in Vegas as Verstappen struggles
Verstappen, seeking to clinch a fourth consecutive drivers' world title with Red Bull, made little impression in a cold and somewhat desultory session and finished 17th, more than two seconds adrift of the pace.
Seven-time champion Hamilton, who finished 10th in Sao Paulo last time out and said he felt like "walking away", clocked a best lap in one minute and 33.825 seconds to outpace Norris by 0.011 seconds.
George Russell was third fastest in the second Mercedes to make it three Britons at the front as Hamilton completed a 'double top' by leading both sessions in cold, dry and slippery conditions in the Nevada desert city.
"Pretty good," said Hamilton, who leaves Mercedes for Ferrari after 12 years at the end of this season.
"It's the first time I've had a day like that this year. The car felt good in P1 and less so in P2 so we have some work to do tonight.
"It's difficult to know why we are where we are, but I am enjoying the track and I hope the car feels the same tomorrow.
"I feel good in myself and I know it's not my driving."
Verstappen said it had been very tricky and his team had work to do to make driving easier.
"Very slippery," said Verstappen.
"These are unique conditions here with the cold but it is the same for everyone.
"We need to understand what need to do. It’s massively tyre-related –- it's like driving on ice."
'Dirty track champions'
Verstappen leads Norris by 62 points with three Grands Prix remaining and will take his fourth title on Saturday night if he finishes ahead of Norris or emerges with at least a 60-point advantage.
Norris, who needs to outscore Verstappen by three points to keep his faint title dream alive, said he had struggled on the streets of the 'sin city' circuit.
"So-so," he said of his session.
"Very slippery. I could have driven a road car faster round there than my F1 car!"
On a cold and dry night in the Nevada desert, the track temperature was only 13 degrees as the second session began in dusty low-grip conditions, Hamilton having led Russell at the top of the opening hour for Mercedes.
That led team boss Toto Wolff to quip that the 'silver arrows' were the "dirty track champions" and they resumed in similar style until Ferrari's Charles Leclerc took control after 20 minutes ahead of Russell.
Russell responded after 28 minutes after switching to softs from mediums with a lap in 1:34.015, four-tenths clear of the Monegasque driver and good enough to resist Hamilton’s lap by two-tenths as the Mercedes pair continued to shine.
Ferrari's switch to softs saw Sainz rise to second before Norris clocked 1:33.836 to go top ahead of Russell by nearly two-tenths followed by Hamilton, relishing the rare conditions, took over in 1;33.825.
At this stage, Verstappen remained on mediums and was down in 17th, clearly not chasing a simulated qualifying lap time as Red Bull struggled for grip. Team-mate Sergio Perez was 19th.
Ferrari also switched back to mediums to do longer runs in race simulation mode as did Red Bull, decisions that may pay dividends, but for Hamilton it was a welcome return to form after a difficult outing at the Sao Paulo Grand Prix.