The 21-year-old lit up the time sheets with a Hungaroring track record, finishing just 0.016 seconds ahead of Bottas with reigning Formula 1 champion Hamilton in third, two tenths back.
Verstappen crossed the line first, his lap greeted with huge cheers from the main grandstand, and despite late improvements by both Bottas and Hamilton, the Mercedes duo were unable to usurp the flying Dutchman.
The Ferrari pair of Charles Leclerc and Sebastian Vettel line up fourth and fifth with Verstappen’s team-mate Pierre Gasly sixth.
Leclerc hit the wall in Q1 after losing control of his Ferrari at the final corner. But swift repairs by his team allowed the Monegasque to carry on.
“The car has felt good all weekend and it was flying in qualifying,” said Verstappen, moments after capturing pole.
“I am very happy about today. There is still a race to do and that is the most important thing.”
Hamilton, who holds a 63-point lead over Verstappen in the standings, said: “We always target first, but it got away from me.
MOST-READ HEADLINES ON talkSPORT.COM
Manchester United target 'sad and angry' at how he has been treated by Juventus
Championship results: Cardiff and Fulham get off to worst possible start
football is back
Nottingham Forest v West Brom live on talkSPORT plus reaction to 3pm games
Man United vs AC Milan live stream: How to watch International Champions Cup clash
Man United legend explains why Dybala could struggle in Premier League
'GOOD, NOT GREAT'
Maguire isn't even the best defender at Leicester, says ex-Arsenal man
Who is O'Neill's replacement at Nottingham Forest set to face West Brom?
Kante fit enough for the bench: Chelsea team news for pre-season clash
“We are in a good position to fight for the win so we will be pushing hard for the victory tomorrow.
“I am always down for a fight. It is a long way down to turn one. It is not easy to overtake but hopefully we can give them a run for their money.”
He is the youngest-ever race winner in F1 but sits 13 points below Ricciardo in this year’s standings, having been hit with three retirements in the first 12 races.
Confirming Ricciardo’s exit, a Red Bull Team Principal Christian Horner said: “We fully respect Daniel’s decision to leave Aston Martin Red Bull Racing and we wish him all the best in the future.
“We would like to thank him for his dedication and the role he has played since joining the team in 2014, the highlights of course being the seven wins and the 29 podiums he has achieved so far with us.”
No announcement has been made on a replacement for Ricciardo at Red Bull.
There are still nine races remaining on the 2018 F1 calendar, which is currently on its summer break.
Ricciardo’s decision to quit comes just days after hinting he was about to sign a new deal with Red Bull ahead of the Belgian Grand Prix in three weeks’ time.
He told Sky Sports: “It will definitely be done by Spa. Whether it gets announced over the summer break or in Spa (I don’t know).
“It’s just a little bit of fune tuning here and there, it’s all good.