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Ronaldo had the first chance of the evening for Portugal when his powerful volley was saved by Kasper Schmeichel.
Danny was next to threaten for the visitors, but after exchanging passes with Ronaldo his strike from the edge of the box was hit straight at the keeper.
Portugal continued to pose the greater threat and Ronaldo fired a shot just wide of the far post after charging through the midfield.
Ronaldo was seeing plenty of the ball for his country and following another powerful run, his cross to the near post was headed narrowly over the bar by Nani.
Against the run of play Denmark came close to taking the lead when Michael Krohn-Dehli curled a low strike from just inside the box onto the far post.
Lasse Vibe had another chance for the hosts just before the break, but his flicked effort did not have enough power to beat the keeper.
Portugal started the second half on the front foot and Ronaldo found himself through on goal, but Schmeichel was out quickly to block his effort.
As the game wore on both teams struggled to create any clear-cut chances until Krohn-Dehli fired a strike narrowly wide of the post.
With the game heading towards a goalless draw, Portugal made the breakthrough five minutes into stoppage time, as Ronaldo headed in Ricardo Quaresma's cross to give his side their first win in qualifying.