"Qualifying is a lot about confidence building and... I was already down and I was struggling through the first sector in every lap," Hamilton told 2009 champion Jenson Button in an interview after stepping out of the car.
"I don't know how, but with some deep breaths I managed to compose myself. Q3 (the final phase) started off the right way but it still wasn't perfect the first lap but still a really clean lap, and the second one even better."
Bottas, five points adrift of his team mate in the championship after three races, could only manage a best effort of 1:24.616.
Hamilton has Ferrari record in sights after sixth Mercedes title
Verstappen was more than a second off Hamilton's pace as the best of the rest, with Ferrari's Charles Leclerc joining him on the second row while his four times champion team mate Sebastian Vettel qualified 10th.
"I think the lap at the end of Q3 was actually pretty good but you could just see pretty early on in qualifying they were just way too fast, as they have been in the last three races," said Verstappen.
The Dutch driver's Thai team mate Alexander Albon failed to make the top 10, continuing a run of poor Saturday form by qualifying 12th.
That places him alongside AlphaTauri's Pierre Gasly, the Frenchman who occupied the Red Bull seat before him.
Gasly missed out on the final top 10 shootout by the slimmest of margins, setting the same time as Racing Point's Canadian Lance Stroll who went through because he did his lap first.
McLaren's British driver Lando Norris will line up in fifth place, ahead of Stroll in sixth, with team mate Carlos Sainz seventh and Renault's Australian Daniel Ricciardo eighth.
Qualifying was held without spectators due to the COVID-19 pandemic.