Albon, 23, walked away unscathed and was given the all-clear by trackside medics, but his team were unable to get his vehicle ready in time.
The Mercedes machines were dominant, with the Ferraris of Sebastian Vettel, third, and Charles Leclerc, fourth, three tenths a second slower, surrendering their speed advantage in Bahrain a fortnight ago. Red Bull's Max Verstappen finished fifth.
"I am OK. More angry and disappointed than anything else".
It was neck and neck on the second runs, but Bottas managed to improve as Hamilton slipped a little in the final sector of his run and Bottas had his first pole of 2019.
The two Renaults were seventh and eighth, with Daniel Ricciardo leading teammate Nico Hulkenberg, while the two Haas drivers failed to set times in Q3 after missing out their runs while being stuck behind the Red Bulls.
Albon, who had looked in with a good chance of making the top 10, said: "I am OK".
"We have fortunately very safe cars", the Austrian explained in the immediate aftermath of the accident.
Albon, who races under the Thai flag, wrote off his Toro Rosso following a 130mph shunt on the exit of the final corner in practice on Saturday morning.
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Bottas said: "It has been a good weekend so far".
Although he will have to start from the pit lane, Albon is hopeful of being able to recover through the field after Toro Rosso showed impressive race performance on Friday afternoon.
Discussing his lap, Bottas said: "It's been a good weekend so far - I felt really comfortable in the practice, but honestly I struggled in Q3 to get a ideal lap". 'I've been fighting the vehicle all weekend, ' he said.
"The lap was ok, not completely how I wanted it but it was good enough for pole and the vehicle has been good enough this weekend and Lewis has improved today too".
Bottas looked strong throughout the weekend and in qualifying, placing a 1:31.547 to go fastest overall.
"To be as close as we are at the end is fantastic".
"I was trying to follow the Ferrari in front of me and trying to overtake him, this time it caught me out and I'm not happy about that", he said.
"I had been playing around with that AstroTurf at the last corner for a while now because it's a bit quicker using that extra bit of track".