Portugal top the group on 18 points, six ahead Denmark and seven ahead of Albania, who lost 2-0 at home to Serbia.
Knowing a point would be enough to see them through to the finals in France, the Portuguese started slowly.
Cristiano Ronaldo forced Kasper Schmeichel into an early save and Nicklas Bendtner blasted an excellent chance over the bar for Denmark.
Bernardo Silva went down in the penalty area midway through the first half, only for the referee to wave away Portuguese appeals for a penalty.
Moutinho put the Danes on alert when he fired a vicious shot from distance, but he could not keep the ball down and it flew harmlessly over Schmeichel's goal.
Nani also went close towards the end of the first half, looping a header over Schmeichel but it bounced harmlessly off the top of the crossbar.
Denmark almost went ahead when Nicklas Bendtner, who has netted six times against Portugal, fired off in early second-half shot which came back off a post.
It was to prove a costly miss as Moutinho broke the deadlock in the 66th minute, collecting a poor defensive header and jinking into position before rifling the ball past Kasper Schmeichel.
The Danes forced a flurry of late corners but they could not force the ball past Rui Patricio and Portugal held on for the win.
Denmark have now completed their qualification campaign and sit out the last match day on Sunday, while Portugal are away Serbia and Albania travel to Armenia where only a win will suffice to snatch second spot.
(Reporting by Philip O'Connor, editing by Ed Osmond)
