"I knew coming into that last Q3 lap, that would be the one that counts, it doesn't matter what happened before then," said Russell, who was fastest in final practice and brushed the wall with his first effort.
"I had a bit of a moment on my first run. We had to change my front wing. There was a moment I thought we wouldn't make the flag.
"You have to put it on the table sometimes. I felt confident in myself and knew if I did a clean lap, I would be on the front row."
The pole was his third of the season and fourth of his career.
Yuki Tsunoda qualified seventh for RB with Norris's team mate Oscar Piastri eighth and Nico Hulkenberg ninth for US-owned Haas.
Seven times world champion Lewis Hamilton, fastest in Thursday practice for Mercedes, was only 10th after misjudging his first effort and running wide before then having his second attempt deleted for exceeding track limits.
"I'm really quite far back so we'll see what we can do from there," said Hamilton.
Verstappen, 62 points clear of Norris with 60 remaining to be won after Las Vegas, had been third after the opening laps with Norris fourth.
The champion's team mate Sergio Perez continued his run of poor form and failed at the first hurdle, qualifying 16th.
Perez has not scored a point since the U.S. Grand Prix in Austin last month and his struggles since May have hit Red Bull hard in the constructors' standings with the champions third overall.
"Unbelievable...I couldn't find any grip," said the Mexican over team radio after being told he was out.
Both Aston Martins also failed to get through the first phase, with Lance Stroll getting only one flying lap after his mechanics raced against the clock to change his car's energy recovery system (ERS) pack.
Argentine rookie Franco Colapinto added to Williams' already hefty repair bill by hitting the wall and crashing in qualifying for the second race in a row.
The crash late in the second phase, which left debris scattered across the track and delayed the session, was the sixth in three races for a team whose boss James Vowles has put the cost at more than $3 million.
The lengthy halt to clean up and make barrier repairs drew a collective groan from the crowd on a chill Nevada night, with qualifying starting at 10 p.m. (0600 GMT on Saturday) and ending well after 11 pm.
The race starts at 10 pm on Saturday.