With the home side seemingly content to sit back and hit on the break, the Danes dominated possession in the first half, and their opening goal came from the last of the nine corners they forced before the interval.
Central defender Simon Kjaer rose highest to head the ball on target and Hannes Halldorsson batted it away, but it bounced off Sigurjonsson and crept over the line, with the referee awarding the goal despite protests from the Iceland keeper.
Sigurjonsson's evening went from bad to worse early in the second half as his side pushed up to try to exploit a long throw.
Despite having his whole team in front of him, the midfielder tried a shot from distance that cannoned off a Danish player and bounced favourably for Eriksen, who snapped up the rebound.
Running from inside his own half, the Danish playmaker outpaced the Icelandic defence before calmly slotting the ball past Halldorsson to double his side's advantage.
The best goal of the night was scored by winger Skov on the hour mark as he kept his balance long enough to curl a brilliant right-foot shot into the top corner to make it 3-0.
Iceland are bottom of the group with no points after three games, having scored only once and conceded nine goals.