The win sends them into second place in Group I level on seven points with leaders Croatia.
In their previous qualifier against Finland, Iceland had to stage a dramatic comeback, scoring twice at the death to win 3-2, but this time they grabbed two goals just before the interval to calm their nerves and allow them to coast to victory.
Central defender Omer Toprak deflected a shot by Elmar Bjarnason into his own net in the 42nd minute and two minutes later Finnbogason scored a stunning volley following a long headed clearance by Kari Arnason down the middle.
The visitors offered little in reply as Iceland continued to enhance their reputation as one of Europe's toughest sides to break down.
Next month they visit leaders Croatia in a meeting of the top two, while Fatih Terim's struggling side seek their first victory in the current qualifying campaign against Kosovo.
(Reporting by Philip O'Connor in Stockholm, editing by Neil Robinson)
