Olafur Karl Finsen scored twice as Stjarnan took full control of their Europa League first qualifying round tie against Bangor City.
Finsen opened the scoring from the penalty spot after Anthony Miley fouled Niclas Vemmelund before Veigar Gunnarsson added a second.
Nine minutes into the second half Finsen scored his second with Arnar Björgvinsson completing the scoring.
Bangor ended the game with ten men after Sam Hart was shown a red card.
Neville Powell's men face the Icelandic side in the second leg at Nantporth on Thursday, 10 July.
The winners of the tie will face Scottish Premier League side Motherwell in the second qualifying round.