The 37-year-old, who retires from Formula One at the end of the season, recorded 1min 39.957 sec to edge out newly-crowned quadruple world champion team-mate German Sebastian Vettel.
Webber, who will start from the front of the grid for only the second time this season, equalled the Australian record of 13 poles set by Alan Jones, who was celebrating his 67th birthday on Saturday.
"Fantastic guys, thank you for a fantastic job," said Webber on the Red Bull team radio.
Hamilton ended up fourth and will start alongside his Mercedes team-mate German Nico Rosberg, who was third fastest.
"Something broke at the rear of the car," said a disappointed Hamilton, who has twice previously taken pole at the spectacular Yas Marina circuit.
For Raikkonen it was a satisfying riposte that demonstrated he retains the upper hand in a team riven by controversy following his threat to boycott the last two races this year because he has not been paid.
Brazilian Felipe Massa, who is leaving Ferrari to make room for the Finn, was eighth fastest - and outpaced his team-mate Spaniard Fernando Alonso for the eighth time this year - ahead of Mexican Sergio Perez of McLaren and 10th placed Australian Daniel Ricciardo of Toro Rosso, who will drive for Red Bull next year.
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