The sprint event, for which there are eight points for a win, seven for second and so on down to eighth place, is on Saturday at 19:00 BST.
The result was a blow to Norris, who needs to close on Verstappen at an average of nearly nine points a race, especially as both Red Bull and McLaren are among the teams with upgrades on their car this weekend.
Verstappen, who had not qualified fastest since the Belgian Grand Prix at the end of July, said: “We had a good day. The car was working quite well and happy to be first. It’s been a while.”
McLaren have had the fastest car for some time, and Verstappen has been fighting a rearguard battle as Norris has eaten into his lead every race since Dutch Grand Prix in late August.
The Briton said: “Not very good. Not a great day. Been struggling the whole day, honestly, with the balance and set-up. In a way, happy with P4 because it could have been a lot worse, but the lap was shocking.”
And he downplayed the relevance of McLaren’s upgrade package, saying: “It’s not a new package, it’s pretty much the same. On pace, we are where we deserve to be.”
Mercedes, on the other hand, had high hopes for their upgrade package, their first significant one for months, and initially it appears to have made a big difference.
Russell said: “Really happy because it’s been a while since we’ve been on on the front row and it was a really tricky session but really pulled the lap together at the end and my last sector was really strong, that’s what made the difference.
“We knew we had potential in the car. The car has been feeling great so far with these upgrades. It’s close but surprised ourselves a little bit with that P2. Just excited to be back in this position. It’s been a little while.”
Both Russell and Hamilton went out early in the session at the Circuit of the Americas, while the other front-runners chose to wait until the last moments.
But this backfired when Williams driver Franco Colapinto, who was the only other driver out on track with them, spun at Turn 12 and Hamilton had to slow down for the subsequent yellow flags.
Hamilton felt the problem had cost him pole position.
“Just got unlucky with the yellow flag, I was 0.4secs up,” the seven-time champion said.
“It is what it is. The good thing is the team has made a step with the car, the upgrade has clearly worked. Really grateful to everyone in the factory. It’s not the end of the day. Tomorrow we have another shot.”
