It is the first time since the introduction of the turbo-hybrid era in 2014 that Mercedes will not start the first race of the season on pole, with Hamilton claiming six of the seven in that period.
Verstappen was seemingly hindered, too, after riding the kerb through turn two on his first flying lap in Q1, causing slight damage to the floor.
Slow-motion replays showed a small chunk of carbon fibre flying from the back of the RB16B on the Dutchman's run down to turn three.
But Verstappen stepped up to the plate when it mattered most, out-qualifying seven-time champion Hamilton by almost four-tenths of a second following a lap of one minute 28.997s.
Verstappen topped the times in every practice session and across all three qualifying sessions for the first time in his 120-race career.
Hamilton was in front after each of his two runs in Q3, but with Verstappen behind, the 23-year-old stole the Briton's thunder and claimed back-to-back poles for the first time - and 105 days apart - given he started the final race of last season in Abu Dhabi at the head of the grid.
Hamilton starts alongside Verstappen on the front row, with team-mate Valtteri Bottas third, with the trio all on the medium-compound tyres.
On the fifth row, Fernando Alonso performed superbly to grab ninth on his Alpine debut, while Lance Stroll starts 10th for Aston Martin.
After his first lap time was deleted in Q2 for exceeding track limits at turn four, Perez was confident enough to again take another set of medium-compound tyres in a bid to make the top 10.
But with the likes of McLaren and Ferrari opting for soft Pirellis for their second runs, it was a gamble that backfired for Perez as the Mexican will start 11th ahead of Alfa Romeo's Antonio Giovinazzi, sparking a flurry of swear words from the Mexican on his return to the pitlane.
AlphaTauri rookie Yuki Tsunoda has caused a sensation in Q1 by finishing second quickest behind Verstappen, but like Perez, a gamble on medium tyres for a second hot lap also failed to work and the 20-year-old Japanese starts 13th.
Alfa Romeo's Kimi Raikkonen lines up 14th, with George Russell 15th, the Briton out-qualifying a Williams team-mate for a 39th consecutive race.
On his F1 qualifying debut, Nikita Mazepin caused a stir as he spun twice, the second of which compromised Sebastian Vettel in his Aston Martin, in particular.
Mazepin lost his Haas on entry to turn one, and with the yellow flags being waved, it forced a number of those behind to slow, notably Vettel.
The four-time F1 champion was then caught out by a second set of waved yellows at turn eight due to Sainz slowing with an engine issue, an incident that also affected Esteban Ocon in his Alpine.
The stewards are to investigate after the session the lap times set during the yellow-flag incidents, but at present Ocon lines up 16th ahead of Williams' Nicholas Latifi and Vettel in 18th.
As was expected, Haas rookie pair Mick Schumacher and Mazepin line up on the back row, with almost a second between the pair.
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