Martin O'Neill's Republic of Ireland side kept a third successive clean sheet to boost their hopes of reaching the World Cup in Russia.
Denmark and the Republic of Ireland drew a blank in Copenhagen as the first leg of their World Cup play-off ended in a 0-0 stalemate.
Fittingly at the Parken Stadium, the visitors dropped deep and defended solidly to keep a third successive clean sheet that puts them in pole position to reach Russia ahead of the return meeting in Dublin.
The Danes struggled to break down their resolute opponents and even when they did occasionally get a sight of goal, Darren Randolph was on hand to keep them out.