Verstappen struck at the death to edge out Valtteri Bottas by just 0.025 seconds to claim the first non-Mercedes pole of the year in dry conditions.
Lewis Hamilton, who missed last weekend's Sakhir Grand Prix in Bahrain with coronavirus, had to settle for third in a closely-fought session under the lights of the Yas Marina circuit. The seven-time world champion finished 0.086secs behind Verstappen.
Formula One is gearing up for its last action of the year following a breathless, coronavirus-disturbed calendar of 17 races within just 24 weeks.
Hamilton wrapped up his record-equalling title in Turkey last month, but after missing the first race of his 14-season career with Covid-19, the Mercedes driver will be keen to capture his 12th win of 2020 on Sunday.
However, he will have his work cut out after Verstappen delivered an imperious lap befitting of an impressive campaign.
Hamilton said: "It has definitely been a difficult weekend in terms of getting back into the rhythm.
"But I gave it my all and congratulations to Max. It is a great way for him to seal a year of good performances. Hopefully, we can give him a good run tomorrow.
"Of course, it is always nice to start first, but you cannot always do that, and that makes tomorrow exciting.
"The start is going to be important, and I am excited as to how I am going to turn it around."
Verstappen said: "I am very, very pleased with the lap. We will wait and see how tomorrow goes and we will try to do our best."
Lando Norris finished an impressive fourth for McLaren, one spot ahead of Verstappen's team-mate Alexander Albon.
Following his heroics last weekend, George Russell qualified only 18th for Sunday's race.
Russell, on loan to Mercedes, missed out on pole in Bahrain by just 0.026 seconds. Here, back at Williams - the British team on course to end another season without a single point - Russell was almost three seconds off Verstappen's pole lap.
Sergio Perez, who took advantage of Russell's misfortune to claim the first win of his career last week, finished 15th but will be thrown to the back of the field for an engine penalty.
Perez will be replaced by Sebastian Vettel at the rebranded Aston Martin team in 2021. In the final appearance of his six-season Ferrari career, the quadruple world champion finished 13th, seven tenths slower than Leclerc, who lines up in ninth.
Vettel has endured a torrid end to his time with the Scuderia and heads into Sunday's final round 13th in the championship, an eye-watering 299 points behind Hamilton and 65 points adrift of Leclerc.
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