Scotland 2-1 Iceland
Lee Wilkie's 70th minute header gave Scotland the win in a game they should have had wrapped up by half time.
Scotland dominated proceedings in the first period but had only Kenny Miller's first international goal to show for it.
But a mistake by Steven Pressley allowed Eidur Gudjohnsen to equalise just after the interval and the Scots found themselves under pressure for the first time.
But Wilkie scored a deserved winner to put Scotland in command in the race for second place in Group Five.
Scotland kept hold of the ball well in the opening five minutes and a Barry Ferguson pass gave Stevie Crawford a half-chance, but his shot on the turn from the edge of the box was easily taken by Arni Arason in the Iceland goal.
Iceland were keeping plenty men behind the ball but a neat one-two between Graham Alexander and Crawford allowed the Preston man plenty of room on the right.
He progressed almost to the bye-line before squaring the ball for Miller to knock the ball past the keeper, giving Scotland the perfect start.
Scotland had been in almost complete control of the game but there was a worrying moment just before the half-hour mark when Gudni Bergsson almost got the break of the ball in the box and it required a last-ditch Steven Pressley tackle to clear the danger.
Don Hutchison should have put the Scots two ahead a couple of minutes later when Gary Naysmith's cross fell kindly for him.
But as Vidarsson desperately tried to prevent Hutchison getting his shot in by pulling him back, the Scotland forward claimed for the penalty instead of shooting, only to see his claim waved away and Alexander eventually drove the ball wide.
A mistake by Larus Sigurdsson almost allowed Crawford in on goal, but the defender was saved by his keeper's outstretched leg.
Naysmith was causing havoc on the Scottish left and he almost headed the Scots further in front when he got on the end of Alexander's cross, but Arason was equal to the effort.
All Scotland's good first-half work was undone three minutes into the second period when Joey Gudjonsson played a pass over the top and, when Pressley rushed out to try to catch Gudjohnsen offside, the Chelsea striker coolly lobbed Rab Douglas to square the match.
Lee Wilkie headed just over from four yards out but was lucky not to give away a penalty when he blatantly pushed Gudjohnsen inside the box a minute later, but to the bemusement of everyone, the referee awarded a free kick inside the box, which came to nothing.
Scotland were rattled and Gudjohnsen should have scored when he met Gudjonsson's cross with his head two yards out, but his effort sneaked beyond the far post.
Ferguson came within inches of regaining the lead for Scotland after an hour, but his drive from 25 yards curled agonisingly wide of Arason's left-hand post.
Scotland slowly regained control of the game but Thorsteinsson had to be halted as he made inroads into the Scotland box.
But with 20 minutes to go, Wilkie headed Scotland back in front after Paul Devlin, a replacement for Hutchison, had sent a teasing cross into the box.
The closing period produced some nervy moments for the Scots, but Vogts' men earned the three points they deserved.
Scotland: Douglas, Wilkie, Pressley, Dailly, Graham Alexander,
Ferguson, Lambert, Hutchison, Naysmith, Miller, Crawford.
Gallacher, Malcolm, Cameron, Gemmill, Gray, Devlin, McNamara.
Iceland: Arason, Thorsteinsson, Larus Sigurdsson, Bergsson,
Gunnarsson, Runar Kristinsson, Johannes Gudjonsson, Ingimarsson,
Vidarsson, Gudjohnsen, Gretarsson.
Subs: Birkir Kristinsson,
Indridi Sigurdsson, Gudmundsson, Marteinsson,
Thordur Gudjonsson, Einarsson, Baldvinsson.
Referee: Rene Temmink (Holland)