The Briton was an unlikely contender to top qualifying after the struggles for the Mercedes W13 all season, not least during both dry and wet running at the Hungaroring so far this weekend.
But despite not taking a fastest sector on his critical lap, his combined runs sailed him to the top over Carlos Sainz, who had the legs on his teammate Charles Leclerc.
But it was a session to forget for Red Bull, with Verstappen only poised to line up 10th as Sergio Perez was eliminated in Q2.
The day-long downpour that was widely predicted held off to allow qualifying to take place as scheduled on Saturday afternoon in Budapest.
It was Sainz who ended the first part of the 12-minute Q3 run on top, his first flying lap placing him half a second clear of Russell after Leclerc had messed up straight away with a snap in his F1-75 at Turn 1 as he struggled with the tyres.
With Verstappen combatting understeer to run off track at Turn 2, he ended the first run-out only seventh fastest.
The 10 fastest cars then emerged with 3m40s to run, but Verstappen was soon complaining of no power aboard his RB18 – cycling through sensor modes not enough to remedy the problem.
With the defending champion, who leads Leclerc in the standings by 63 points, out of the picture, Sainz cycled to the top with the fastest first sector of anyone (pipping Nicholas Latifi).
That gave the British GP polesitter the bragging rights initially as Leclerc slotted in 0.15s adrift, but then three personal best sectors at the death for Russell gave him an unlikely pole.
His 1m17.377s effort pipping Sainz’s 1m17.421s best, while Leclerc managed to keep ahead of the McLaren of Lando Norris – the MCL36 impressing in dry qualifying and race simulations during FP2 on Friday.
Esteban Ocon managed to reverse the recent run of form to pip Fernando Alonso in the intra-team Alpine scrap, while Lewis Hamilton’s DRS failed to activate on his final lap to knock him to seventh.
Valtteri Bottas claimed eighth ahead of Daniel Ricciardo, as Verstappen had to make do with a 1m18.823s that left him 10ths and 1.5s adrift of the Mercedes benchmark.
Perez was the major casualty from Q2 in a strange session for the driver, his Red Bull being knocked out by a slender 0.05s courtesy of the late improvements from Ocon and Bottas.
The Mexican complained that Kevin Magnussen’s line through the Turn 3 left-hander had ultimately cost him a place inside the top 10.
Perez had his first lap in Q2 scrubbed off for exceeding track…
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