Verstappen had begun the weekend seemingly resigned to being third fastest at best, to a point where he took the third-place chair with him from the Thursday press session.
"So many times this year we've sat in that third-place seat," said Horner. "Max actually took it home with him at the press conference on Thursday but he's just strung together a brilliant lap at the end there.
"It's so tight, less than a tenth between the top three cars. He was gutted to miss out last week and to put that lap together to get that pole was a phenomenal performance.
"You know you can bank on him and you know he's going to give it everything. You know that he can always surprise you and he's done that today going into that qualifying.
"I thought P3 looks comfortable but you can see from the reaction what it means to the team and the team has worked their nuts off this year. We've had nine of the 10 fastest pit stops of the season and they've been remarkable."
Red Bull has steadily closed the gap to Mercedes across the year and with a large amount of carryover between the 2020 and 2021 cars, Horner said scoring pole on the final weekend of the year is an "important" result.
Horner added: "I think for the team that have just worked so hard to keep improving this car, I think for Honda as well, and for Max who has just been mighty this year and he has dragged every ounce of performance out of the car - to get this pole at the last race is important.
Sunday will provide a different challenge for Red Bull if they are to add to their one race victory this year, which came when Verstappen won the 70th Anniversary Grand Prix in the fourth race of the year.
Horner expalined: "It's important to convert it tomorrow into a great result so I just think for everybody in the whole team they have just worked so hard under such difficult conditions this year."
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