Triple world champion Hamilton qualified alongside, a mere 0.023 - or 17 centimetres - slower than Bottas's time of one minute 28.769 seconds but with everything still to play for on Sunday.
That clinched the first front row lockout of the season for the reigning champions after two races with Ferrari's Sebastian Vettel splitting the Silver Arrows.
Hamilton, joking and laughing in a later news conference, appeared delighted for Bottas and offered a warm handshake to a man who left China last weekend with his mind in turmoil after a costly mistake behind the safety car.
"Firstly, a big congratulations to Valtteri. He has been working so hard, gelled so well with the team and today he was just quicker, he did the better job and hats off to him," said Hamilton.
"That's how close I think qualifying should always be. It forces us all to be more on the limit."
"For sure, it feels good," said Bottas, the first Finnish driver to secure a pole position since Hamilton's then-team mate Heikki Kovalainen for McLaren at the 2008 British Grand Prix, 168 races ago.
"It's my first pole in my career in my fifth season in F1 so it took a few years but hopefully it's the first of many for me," he added.
Vettel, joint leader of the world championship standings with Hamilton after two races with one win each, will start in third place with Red Bull's Australian Daniel Ricciardo fourth.
Ferrari's Kimi Raikkonen, whose last pole was also in 2008, qualified fifth.
Mercedes won the race last year with now-retired champion Nico Rosberg, the man Bottas has replaced, and have now taken five successive poles at the desert Sakhir circuit.
Hamilton had been fastest in both the first and second phases of qualifying, and set the pace with his first lap in the final session before Bottas pulled off his masterstroke.
The unflappable Finn let out a rare whoop over the team radio, with engineer Tony Ross -- who had inadvertently called Bottas 'Nico' during the race in China -- replying that "for a moment there you actually showed some emotion, well done".
Hamilton and Vettel, sitting alongside Bottas in front of reporters, jokingly asked the polesitter whether the Finnish language had a word for 'excited' or 'exciting'.
Bottas thought hard but words failed him. "Kind of," he hesitated, as his rivals laughed.
"See, it doesn't exist," said Vettel. "It's not one that's really used much in the vocabulary," added Hamilton.
"I don't know really," concluded Bottas.
Dutch teenager Max Verstappen qualified sixth for Red Bull with Nico Hulkenberg seventh on a good day for Renault, who had Britain's Jolyon Palmer in 10th place after his first appearance in the final phase.
Brazilian Felipe Massa starts eighth for Williams and France's Romain Grosjean ninth for Haas.
German driver Pascal Wehrlein also made a strong return after a back injury kept him out of the first two races, qualifying 13th for Sauber while Swedish team mate Marcus Ericsson was only 19th.
(Editing by Ed Osmond and Ian Chadband)
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