Goals from Lasse Schøne and Christian Eriksen earned Denmark victory in Iceland, a result which moves the visitors onto ten points at the top of Group H alongside Portugal and Norway.
Chances were few and far between in a tight and often cagey opening period before Morten Olsen's half-time substitution proved to be the difference. Schøne came off the bench to open the scoring with a well-struck shot from the edge of the area before Eriksen, a constant threat for the visitors, slotted past Stefán Magnússon to seal the points 15 minutes from time.
The Danes controlled the game from the start but were unable to find a way past a resilient Iceland defence in the first half. Schøne replaced Michael Krohn-Dehli at the break and took just 15 minutes to make an impact.
The 25-year-old picked up the ball on the edge of the area and unleashed an unstoppable strike to put his side ahead. Highly-rated AFC Ajax midfielder Eriksen was always a threat with his pace, meanwhile, and he made sure of the points for Denmark, finishing neatly from Dennis Rommedahl's right-wing cross.
Iceland travel to Norway on 2 September before Denmark face the same opposition in Copenhagen four days later.