Norris’ team-mate Oscar Piastri was knocked out in the first session because his lap time was deleted for exceeding track limits at the penultimate corner and will start the sprint 16th.
Red Bull’s Sergio Perez was knocked out in the second session and will start 11th.
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.”
More to follow