The Real Madrid forward rose magnificently to head home a cross from Ricardo Quaresma five minutes into time added on, earning a welcome first win for Portugal's new coach Fernando Santos.
Portugal lost their opening match in qualifying Group I 1-0 at home to Albania last month, a result that led to the departure of former coach Paulo Bento.
And they then went down 2-1 to France in a friendly on Saturday in their first game under Santos.
Albania, whose game with Serbia was abandoned before half-time in Belgrade on Tuesday after an incident involving a drone, still top Group I with four points from two games, above Denmark on goal difference, while Portugal are a point back.
With the Danes dominating, Portugal saw Michael Krohn-Dehli's 34th-minute shot hit a post to send the teams in 0-0 at half-time. And the game looked destined to end in a stalemate before Portugal's talisman grabbed the winner and the headlines at the death.
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