The defending double world champion and series leader outpaced the Hulkenberg by 1.244 seconds in a very wet top-ten shootout to secure his 25th career pole.
It also completed a hat-trick for the Dutchman after poles in Monaco and Spain.
It was set to be the third front-row starting position for Hulkenberg and the first for the American-owned Haas team before he collected a three-place penalty for an infringement in qualifying and dropped to fifth.
"The regulation is very clear and whilst there is no question of the driver acting dangerously or driving unsafely, there was a breach and thus a penalty has to be imposed," stewards said in a statement.
"The normal penalty for failure to slow under red flags is 10 grid positions however in view of the mitigating circumstance, a lower penalty is appropriate.
"We note the intention of the regulation is to ensure a car is not speeding during a red flag situation and there is no evidence that the speed was excessive in this case."
Two-time champion Fernando Alonso - who was third-fastest - will start in second for Aston Martin. Seven-time champion Lewis Hamilton of Mercedes will start from third.
George Russell will start in fourth in the second Mercedes. Behind Hulkenberg in fifth are Esteban Ocon of Alpine, Lando Norris of McLaren and Oscar Piastri in the second McLaren.
Carlos Sainz of Ferrari was due to start eighth, but received a three-place penalty of his own for impeding Pierre Gasly.
Alex Albon was 10th for Williams while both Red Bull's Sergio Perez and Ferrari's Charles Leclerc failed to proceed from Q2 for the second consecutive event.
"We made changes after a tricky day yesterday, said Verstappen.
"And it was completely wet but the car felt improved to drive. In these conditions, you have to stay on top of everything as it is super-slippery and but we made all the right calls and I am very happy to be on pole here.
"I'm from Holland so I like driving in the wet."
Hulkenberg said: "It was a wild and crazy session in changing conditions with the walls so close in the wet – we were changing tyres and the team did a great job."
Alonso admitted it had been a difficult session in which to choose the right tyres at the right time.
"But we have P3 and we will take that," he said.
"The fans here are amazing and the city embraces the Grand Prix so I hope they all enjoyed it. If we push, we have a chance tomorrow."
After his crash in final practice, Sainz was relieved to learn his Ferrari was repaired in time for qualifying and that, despite a call to the stewards' office, he faced no penalty for allegedly impeding Albon.
As in 2022, the qualifying session began in cold and damp conditions with an air temperature of 16 degrees and the track at only 18, insufficient to generate optimum tyre temperatures for most teams, notably Mercedes.
The two Williams of Albon and American rookie Logan Sargeant led the way into Q1 as Zhou Guanyu pulled up in his spluttering Alfa Romeo, prompting a red flag.
Zhou made it back to the pits and after repairs was in the queue when the session re-started after six minutes as rain was reported arriving at Turn Two.
This turned it into a race against the weather in which Verstappen and Alonso swapped quickest laps and others, including Hamilton, Leclerc and Perez, took to escape roads.
In a final flurry, Verstappen was quickest ahead of Alonso as out went Alpha Tauri's Yuki Tsunoda, Alpine's Gasly, Nyck de Vries in the second Alpha Tauri, Sargeant and Zhou.
Albon boldly took the gamble on slicks for Q2, with rain forecast to arrive after six minutes. Ferrari more cautiously asked Leclerc to stay on intermediates for an early "banker" lap.
More rain
Verstappen and the rest then switched to slicks as Albon went top - and the rain arrived.
Unperturbed, Albon trimmed his time to 1:18.725 while Mercedes unhappily remained on intermediates before Hamilton was finally switched to slicks.
As Hamilton squeezed into 10th, both Leclerc and Perez faced a second consecutive elimination from Q2, their teams having failed with their strategy.
It was the first time Williams had topped a qualifying segment since Felipe Massa in Belgium in 2016.
Leclerc and Perez joined Lance Stroll, Haas's Kevin Magnussen and Bottas in missing the top-10 Q3 shootout as the rain intensified and Verstappen led the way on intermediates.
The session was red-flagged after five minutes when Piastri crashed his McLaren at the exit of Turn Six, smacking the wall and damaging the rear end.
This left Verstappen leading the way ahead of Hulkenberg, in his Haas, and Alonso's Aston Martin with Hamilton and Russell fourth and fifth for Mercedes – and the track awash after more heavy rain.
