Hamilton had appeared on course to take the 98th pole of his career after improving with his final run, but Bottas went even quicker in a nail-biting session to take the spoils.
Hamilton heads into Sunday's round 77 points clear of Bottas and another triumph here will pave the way for the Englishman to equal Michael Schumacher's record of seven titles at the ensuing race in Turkey on November 15.
But the 35-year-old will have to pass Bottas after the Finnish driver claimed a hat-trick of pole positions. He will now be searching for just his third win of the campaign on Sunday to keep alive his miniscule title chances.
This marked Mercedes' 13th pole in as many rounds and they will secure their seventh constructors' championship here on Sunday with four rounds remaining if they outscore Red Bull.
It is a feat they have achieved at every round since Hamilton and former team-mate Nico Rosberg took each other out of the Spanish Grand Prix more than four years ago.
Verstappen was in danger of being knocked out in Q2 following a spark plug failure.
But his Red Bull crew rectified the problem and Verstappen required just one flying lap to haul his car into the final phase of qualifying before slotting into his customary position behind the Mercedes drivers, albeit half-a-second down.
Charles Leclerc finished seventh for Ferrari at the Italian team's third home round of this Covid-disturbed campaign. British driver Lando Norris was eighth in his McLaren.
George Russell's future has been in some doubt following speculation that Williams' new owners would replace the young Briton with a driver who brings significant cash to the team.
But ahead of this weekend's race, Williams put to bed those rumours by rubber-stamping Russell's seat for 2021, and the impressive Englishman delivered once over one lap to finish 13th and extend his unbeaten qualifying run against his team-mates to 34.
Four-time world champion Sebastian Vettel starts one spot behind the Williams driver in a miserable 14th for Ferrari.