Williams driver Russell ousted Lewis Hamilton from top spot on the grid in the dying stages of a stunning qualifying session but was denied by Verstappen at the death as the Red Bull title contender claimed the ninth pole of his career, and his team's first at Spa for 10 years.
It was a remarkable performance from Russell who has thrust himself firmly into the mind of Mercedes boss Toto Wolff for the second seat with the Silver Arrows as he beat a driver in Hamilton who is widely regarded as the best in the wet.
Hamilton will start third ahead of McLaren's Daniel Ricciardo, whose team-mate Lando Norris was in the medical centre when qualifying concluded after his crash earlier in the Q3.
After the first two sessions had been run on a wet track but with the cars requiring only the intermediate tyres, heavy rain again fell before the start of Q3.
At one stage, Aston Martin's Sebastian Vettel called for a red flag, while Norris said he had suffered a lot of aquaplaning on his out lap before setting off on his flier.
But emerging out of the compression through Eau Rouge, Norris lost the back end of his car up the hill towards Raidillon.
The Briton then ploughed into a tyre wall to his left, bouncing off and sending him into a number of pirouettes back across the track before finally coming to rest at Raidillon.
It immediately led to the session being red-flagged, which Vettel had called for a minute earlier.
Upon being told the session had been stopped due to Norris' shunt, an angry Vettel said: "What the f**k did I say? What did I say? Unnecessary! Is he okay?"
Vettel was then first upon the scene of Norris' crash, pulling over and giving him the thumbs-up sign to check if he was uninjured. The Briton responded with a thumbs up of his own before apologising to the team for his mistake.
Torrential rain followed and after a 42-minute delay the remaining nine drivers took to the track, with the majority on inters - including both Mercedes and Red Bull drivers - despite the huge plumes of spray behind them.
Yet the drivers somehow mastered the appalling conditions, notably Russell who confirmed saving up all his battery power for his flying lap.
That means a start from 13th on the grid for Bottas who serves a five-place penalty for causing the first-corner carnage in the last race in Hungary.
Alpine's Esteban Ocon starts ninth, with Norris currently 10th, although given the damage to his car it is likely he will start from the pitlane.
Heavy rain had fallen ahead of the session which led to what turned into an initial 12-minute delay following a safety car inspection by Bernd Maylander.
During that hiatus, Mercedes fitted a small gurney flap to the rear wing of its W12s, designed to provide additional rear downforce in the wet, albeit with the offset being a little extra drag.
The conditions, though, still proved to be a great leveller in the opening laps, but with Russell and Nicholas Latifi the only drivers to take to the circuit on intermediate tyres while the other 18 were on full wets.
It proved to be the right call as the duo initially topped the timesheet, sparking a flurry of stops by the rest of the field to change rubber with around six to seven minutes remaining.
By the conclusion of Q1, there were no major surprises, although maiden grand prix winner last time out in Hungary in Ocon just avoided the drop zone, finishing 15th, half-a-second clear of Alfa Romeo's Antonio Giovinazzi.
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