Australia's Ricciardo, embarking on his first race with Red Bull, stormed to the top of the field on his last run, before he was trumped by Mercedes' Hamilton in a flying final lap in treacherous wet conditions.
The 2008 world champion's German team-mate, Nico Rosberg, placed third, with McLaren rookie Kevin Magnussen fourth and Ferrari's Fernando Alonso fifth in the season's first qualifying session.
But there was a sensational miss for Vettel, seeking his fifth straight world title and record 10th consecutive race win, who failed even to reach the final qualifying shoot-out and will start from 12th.
"It's been an interesting weekend and today made it so much more harder for everyone with the conditions," Hamilton said.
"But I'm really happy with what the team did and these new cars are a lot harder to drive in the wet -- it was the first time for me driving in the wet (in the new car) so it was a serious task and challenge today."
It was the first time since Abu Dhabi in 2012 that Vettel has missed Q3, while Hamilton's pole position ends Red Bull's run of eight consecutive races after the Belgian Grand Prix in August.
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