Ronaldo rose to meet Ricardo Quaresma's cross and bury his header past Kasper Schmeichel to claim all three points after referee Felix Byrch played five minutes stoppage time at the end of the game.
Denmark's best chance of the match came when Pierre Hojbjerg muscled his way through and fed Christian Eriksen, who teed up Michael Krohn-Dehli to fire in a shot that came back off the far post.
Ronaldo's goal lifts Portugal off the bottom of the table and into third in the five-team group on three points. Denmark remain second, level on four points with leaders Albania.
Portugal coach Fernando Santos praised his captain after his late goal, saying: "Cristiano is Cristiano. He is a winner, and there are no adjectives to describe him."
Ronaldo announced his presence as early as the seventh minute with a thumping shot on target before teeing up Danny six minutes later. Both efforts were saved, however, by Schmeichel in the Danish goal.
Denmark lost defender Nicolai Boilesen 10 minutes into the second half when the left back was stretchered off having been knocked out cold by a thundering clearance from Daniel Agger.
The Danes enjoyed plenty of possession after that, passing well on the slick, rain-soaked Parken pitch, but despite being roared on by a sell-out crowd of 36,562 they rarely threatened the Portuguese goal and were eventually punished.
"We knew that Denmark were very strong," Santos told reporters. "I think they saw the match against France and changed from their normal tactics, from a 4-3-3 to 4-4-2 trying to control the match.
With time running out, Ronaldo took centre stage, first enduring the jeers of the crowd as he was yellow-carded in the final minute for a tackle on Hojbjerg, before scoring the game's decisive goal a few minutes later.
An angry Denmark coach Morten Olsen hammered his side for their lapse in concentration that led to Ronaldo's goal.
"You have to know the last five minutes you have to play with discipline and concentration so that these things don't happen," he said.
"You have to be professional, these are very important points that we lost here."
(Reporting By Philip O'Connor; editing by Toby Davis)
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