A Gylfi Sigurdsson penalty on 51 minutes ensured that Iceland stay top of Group A with 18 points - eight ahead of World Cup bronze medallists the Netherlands - who are third with three games left.
The stuttering Dutch campaign had already cost Guus Hiddink his job and new coach Danny Blind had a baptism of fire in Amsterdam.
With their backs to the wall the Dutch desperately needed a win but were lucky not to be trailing after seven minutes with Jon Dadi Bodvarson missing on front of goal.
And things began to unravel for the hosts when defender Bruno Martins Indi was send off on 33 minutes for appearing to grab striker Kolbeinn Sigthorsson by the neck.
The nightmare continued after the break with Swansea midfielder Sigurdsson converting a penalty awarded after Gregory van der Wiel brought down Birkir Bjarnason.
Blind, the former iconic captain of Dutch giants Ajax, had said he wanted to "breathe new life" into the national side, but time is now ticking on the 1988 European champions' campaign.
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