Gylfi Sigurdsson settled their nerves with a superbly-taken goal five minutes before halftime as Iceland proved that their run to the 2016 European Championship quarter-finals, which included wins over Austria and England, was no fluke.
Sigurdsson also set up the second for Johann Gudmundsson midway through the second half as Iceland completed the campaign by winning their final three games without conceding a goal.
It was a remarkable achievement for a country which has a population of about 350,000. The previous smallest country to have reached the finals was Trinidad & Tobago, in 2006, with 1.3 million people.
Coached by part-time dentist Heimir Hallgrimsson, Iceland finished the group with 22 points from their 10 games.
Until fireworks went off after the final whistle, Monday’s match on a wet Reykjavik night rarely felt like an historic occasion, with the hosts grinding out a routine win against opponents who were more refined technically but lacked punch.
Iceland's starting lineup included four players based in England's second tier, two from the English Premier League, one from Italy's Serie A and one each from the top flights of Denmark, Sweden, Scotland and Russia.
An emphatic 3-0 win in Turkey on Friday had sent Iceland top of the group for the final match, although they struggled to impose themselves against the group's bottom side.
Iceland had to wait half an hour for their first real chance when Jon Bodvarsson's far post header was easily saved by Samir Ujkani.
Milot Rashica gave Iceland a fright with a long-range shot which flew past Hannes Halldorsson's post but Iceland went ahead with their next attack and their first shot on target.
Sigurdsson collected the ball on the edge of the area, wriggled his way past Amir Rrahmani and fired beyond Ujkani for his fourth goal of the qualifiers.
Iceland were happy to sit on their lead but struck again in the 68th minute when Sigurdsson again got past Rrahmani and laid the ball into the middle for Gudmundsson to score from close range.
Iceland's seven wins in the group included all five of their home matches where previous World Cup semi-finalists Croatia and Turkey were among the victims.
(Reporting by Brian Homewood; Editing by Ken Ferris)
