Bristol City defender Magnusson put the visitors ahead halfway through the first period after an otherwise uneventful start with his free-kick surging over the wall into the bottom corner as he scored his first international goal.
With injured captain Seamus Coleman sitting out, Robbie Brady was given the armband as an altered Ireland lineup struggled for chemistry as Iceland keeper Ogmundur Kristinsson had an uneventful night, not being forced to make any saves as the visitor's defence held firm.
With both teams second in their 2018 FIFA World Cup qualifying groups, Iceland are looking the more likely of the duo to reach the tournament in what would be their first appearance in the competition.
Conor Hourihane and John Egan were given their international debut's by Martin O'Neill, with the latter's first appearance marked by an elbow to the face, needing a bandage to stop the bleeding, before being booked for taking down Kjartan Finnbogason after 20 minutes as Iceland scored from the resulting free-kick with the first shot of the match.
Magnussen's superb strike floated over the wall before dipping into Keiren Westwood's bottom-left corner, giving the Sheffield Wednesday keeper no chance of making the save.
Aron Gunnarsson and Finnbogason came close to extending the lead while Kevin Doyle headed wide from a James McClean's cross after 36 minutes as an experimental Ireland side were unable to muster any shots on target in the first half.
While Ireland improved after the break, forcing the visitors into making a number of clearances they were unable to convert with their long unbeaten run at home ended ahead of a qualifier in June against Austria, while Iceland next face Croatia.