Heimir Hallgrimsson's team knew a win against Group I's bottom side would guarantee top spot and an automatic qualifying place, and Everton's Gylfi Sigurdsson settled their nerves with a superbly taken goal five minutes before half-time.
Sigurdsson also set up the second for Johann Berg Gudmundsson midway through the second half as Iceland completed the campaign by winning their final three games, proving their run to the quarter-finals of Euro 2016 was no fluke.
An emphatic 3-0 win in Turkey on Friday, October 6 had sent Iceland top of the group before the final match, but they struggled to impose themselves against the group's bottom side. Jon Bodvarsson's far-post header was easily saved by Samir Ujkani, before Milot Rashica gave Iceland a fright with a long-range shot which flew past Hannes Halldorsson's post.
With their next attack, Iceland went ahead. 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. The hosts were happy to sit back on their lead until Sigurdsson again got past Rrahmani and crossed for Gudmundsson to make sure of victory in the 68th minute.
Hallgrimsson, a part-time dentist who became sole manager after Euro 2016, when Lars Lagerback left to take the Norway manager's job, was lost for words at the final whistle.
"This is really odd, I don't know what to say. I mean ... Peleacute;, Maradona, Aron Einar Gunnarsson," Hallgrimsson said, referencing the Cardiff midfielder at the heart of his side.
Qualification for their first World Cup is a remarkable achievement for Iceland, a country with a population of approximately 335,000. The previous smallest country to have reached the finals was Trinidad amp; Tobago in 2006 (1.3m people) followed by Northern Ireland (1.85m), Slovenia (2.08m), Jamaica (2.89m) and Wales (3.1m).
Armenia, playing in Group E, collected seven points only and did not manage to qualify for the finals. Poland, meanwhile, qualified.