However, former Chelsea man Eidur Gudjohnsen reduced the deficit with just over ten minutes remaining when he converted a penalty after Stephen McManus was sent off for handling in the box. Scotland held on to their lead despite a nervy finish to claim their first points of the campaign and give George Burley his first win as manager.
Iceland dominated the early encounters and created a host of chances in the opening period. In the 11th minute Birkir Saevarsson released Aron Gunnarsson down the right wing. The Coventry player cut into the box and Craig Gordon had to be at his best to beat away his powerful effort.
Barcelona forward Gudjohnsen should have put Iceland ahead in the 16th minute. Saevarsson found him unmarked in the box with a delicate chipped ball but he went for the spectacular and he blazed his first-time effort well over.
Scotland rallied, however, and it was they who took the lead after 18 minutes through Broadfoot. The Rangers defender, who had earlier been booked for a late tackle on Eriksson, got on the end of a Barry Robson corner and powered home a header past Kjartan Sturluson for a dream debut.
The Scots were on top as half-time approached and Kristjan Sigurdsson had to stretch to make a desperate interception from a Shaun Maloney cross with McFadden lurking at the back post. With 40 minutes gone Kris Commons broke down the right and his deep cross was put out for a corner by an Iceland defender before McFadden could get apply the finish.
Iceland started the second-half brightly and Gordon had to stretch to tip Kristjan Sigurdsson's looping effort over the bar shortly after the re-start.
However, it was Scotland who doubled their lead on the hour mark after McFadden was scythed down in the box by Sigurdsson. The Birmingham City striker took the resulting penalty and although his effort was well-saved he managed to bundle the resulting rebound into the net just in front of Robson as the Icelandic defence stood static.
The Scots were on top at this stage but things turned sour for them when they were reduced to ten men in the 76th minute. Captain McManus saw red for handball to sour his 26th birthday and Gudjohnsen scored the resulting penalty, sending Gordon the wrong way with a powerful right-footed kick.