A stunning final lap from Russell looked set to give the Williams driver a first career pole, but Formula 1® title hopeful Verstappen pipped him in the closing seconds.
British 23-year-old Russell, who has been tipped for a move to join Lewis Hamilton at Mercedes next season, said he was "absolutely buzzing" about his performance, defying the limitations of his car with a supreme drive.
Hamilton took third on the grid and saluted Russell's performance, with Daniel Ricciardo fourth.
The qualifying session was disrupted by heavy rain and a heavy crash for Lando Norris – Ricciardo's McLaren team-mate – which caused a hold-up in Q3 of close to 45 minutes.
Moments before smashing into the barriers, Norris complained about the conditions, and Sebastian Vettel had called for the session to be red-flagged before the crash made it an inevitability. Norris was taken to the hospital for a precautionary elbow X-ray.
The drivers returned to the wet track eventually, with Hamilton quick to point out that spray remained a problem. He set an early target of 2:01.552 but Russell producing a stunning lap to go quicker.
Verstappen and Hamilton were both out on the track and chasing the new target as the clock ran down, with only the former able to achieve that.
After three weeks since the last race, the Hungarian Grand Prix, this was a return to the thrills and spills of the sport.
"I'm super happy to have a qualifying like this after the break and to have a pole position again," said Verstappen.
Russell has been on the front row once before, but that came in a Mercedes when he stood in for Hamilton last season at the Sakhir Grand Prix. He said getting out of Q1, the initial stage of the qualifying session, had been his primary target at Spa, with anything else a bonus.
"The car was feeling great and I had so much confidence," Russell said. "I was in a fortunate position where I had nothing to lose. We were in Q3 which is not the norm for us and we just had to go for it.
"I'm buzzing, absolutely buzzing. Tomorrow's the important one but it's been mega today. I'm delighted for everyone. If the weather is the same and it's there for the taking tomorrow, we'll go for it."
Hamilton, who edged ahead of Verstappen in the drivers' standings by finishing second in Hungary, said it had been "a very difficult day for everyone" due to the inclement weather.
"Well done to Max and to George," Hamilton added. "If it's like this tomorrow it's going to be tricky to balance straight-line speed and downforce."
1. Max Verstappen (Red Bull) 1:59.765
2. George Russell (Williams) +0.321secs
3. Lewis Hamilton (Mercedes) +0.334
4. Daniel Ricciardo (McLaren) +1.099
5. Sebastian Vettel (Aston Martin) +1.170
6. Pierre Gasly (AlphaTauri) +1.399
7. Sergio Perez (Red Bull) +2.347
8. Valtteri Bottas (Mercedes) +2.737
9. Esteban Ocon (Alpine) +3.748
10. Lando Norris (McLaren) no complete lap in Q3