Walter Mazzarri's men had too much class for their opponents in Reykjavik, with goals to Mauro Icardi and Dodo either side of half-time building an imposing lead for the Italians before Danilo D'Ambrosio added a third late on.
The visitors were rewarded for their first-half dominance at the Laugardalsvollur when Icardi finished off a dinked cross in from Dodo - with the Stjarnan defence unable to deal with it.
Dodo then doubled Inter's lead shortly after the interval, nodding home Jonathan's cross at the far post - and D'Ambrosio capped a complete performance in the 89th minute.
Dodo and Icardi earlier combined to create the first chance of the game in the third minute, with the former's corner finding the Argentine in the area – but his header went high over the crossbar.
The Brazilian full-back then turned scorer, netting a header from fellow full-back Jonathan to strengthen Inter's position.
Making his competitive debut for the club, Dani Osvaldo hit the woodwork late on after coming on as a second-half substitute, before D'Ambrosio smashed a ball home into the roof of the net after Zdravko Kuzmanovic played him through.
In Wednesday's other Europa League play-off, Yevhen Shakhov's dramatic late winner helped Dnipro Dnipropetrovsk defeat Hajduk Split 2-1 in Kiev.
