Ferrari's Charles Leclerc and Carlos Sainz turned out to be the closest challengers in third and fourth with Fernando Alonso, who made waves with his pace in practice, lining up fifth for Aston Martin.
Red Bull came to Bahrain as favourites after winning 17 of 22 races last year and being quick in testing. But their struggle for balance, while Alonso set the practice pace, had encouraged others' dreams of a different battle.
Instead, Verstappen found the time when he needed it to deliver the perfect 51st birthday present for his father Jos with a career 21st pole.
"I hope he was watching, I'm pretty sure he was watching," he said.
"It's been a bit of a tough start to the weekend yesterday and today not really finding my rhythm, but luckily in qualifying we managed to put the best pieces together.
"I was actually positively surprised we were on pole after the struggles I had in practice," he added. "Normally our race car is better, so let's see."
FERRARI FAST
Ferrari, runners-up last season and under the new management of Fred Vasseur, showed also that they remained in the mix despite suggestions they might have fallen back.
Sainz was fastest in the first phase of qualifying and Leclerc top in the second, with Verstappen seventh and second respectively.
Leclerc then did only one flying lap in the final phase, opting instead to get out of the car before the end of the session and save a set of new tyres for a race at a circuit with a particularly abrasive surface.
That move allowed Perez to jump from third to second, while Sainz could only manage to leapfrog double world champion Alonso, the oldest driver on the grid at 41, with his final effort.
"I think we were in the fight for pole, which was a good surprise to be honest," said Leclerc. "I don't know if I would have been on pole or not but it would have been close."
Mercedes qualified sixth and seventh with George Russell and seven times champion Lewis Hamilton running out of tyres for the final phase.
"Today was a lot better than we expected," said Russell. "We had a tough Friday; we expected to add a little bit of performance overnight, but we exceeded expectations.
"We are in a good place to fight for third. Qualifying three tenths behind Ferrari when they have probably been the fastest car on single-lap pace is positive. Fernando is probably more of a dark horse than Ferrari."
Alonso's Canadian team mate Lance Stroll, who broke his wrists in a cycling accident in Spain last month and missed testing, will start eighth.
"It's exactly two weeks today since my accident. I couldn't move both hands, couldn't walk. I had a broken big toe on the right foot as well," he said of his journey from hospital to top 10 on the grid.
Esteban Ocon qualified ninth for Renault-owned Alpine and Nico Hulkenberg, starting his first full season since he was at Renault in 2019, a strong 10th for Haas.
American Logan Sargeant was the highest qualifier among the three rookies, placing his Williams 16th on the grid with team mate Alex Albon 15th.
Australian Oscar Piastri will make his debut in 18th place for McLaren, who also have Lando Norris in 11th.
The Briton said it was still "a little bit better" than he had expected.
