The Portuguese, however, almost let victory escape their grasp as Cristiano Ronaldo squandered two chances that could have put the result beyond doubt in another miserable international game.
With Ronaldo misfiring, the Danes fought back to 2-2 with goals in each half from Nicklas Bendtner, who provided a lesson in clinical finishing.
"We should have killed the game off earlier," Portugal coach Paulo Bento said. "We had enough chances."
Substitute Silvestre Varela scored the winner three minutes from the end, spinning on the ball and shooting from short range to revive Portugal's hopes of reaching the quarterfinals after a 1-0 loss to Germany in its opening game. It was Varela's first international goal in four appearances.
Portugal went into the game on the back of a four-game winless streak when it found the net only once, dimming hopes that a team featuring some of Europe's top club talent could produce its best form at the tournament.
Central defender Pepe scored with a header in the 24th minute and Helder Postiga met a cross from Nani to score his first goal since November from short range in the 37th.
Bento ran screaming and jumping along the touchline in celebration, relieved his team had started hitting the target after playing well but wasting opportunities against the Germans.
"We were much better at finishing today," said Bento, who team now has three points, the same as Denmark.
Even so, Portugal could have opened a bigger advantage as Postiga and Ronaldo missed clear chances and Denmark battled level with goals from Bendtner just before halftime and then 10 minutes from the end.
"We suffered too much," Bento said. "We could have won more comfortably."
The Danes, whose compact defense shut out the Netherlands in a surprise 1-0 win in its first match, had few openings in attack but expertly took the chances they had.
"Conceding an equalizer so late, we showed great strength of character to keep going after the win," Bento said.
Ronaldo, who scored 60 goals for Real Madrid last season, looked on dejectedly.
He didn't take a shot until the 18th minute. That flew wide, and the world's most expensive player threw his arms in the air and apparently cursed at a divot in the pitch.
His best chances came in the second half. He broke through the Danish defense five minutes after the break and ran at Stephan Andersen, who dived sharply to his left to block the shot.
In the 78th, Ronaldo was guilty of another astonishing miss when he went face-to-face with Andersen but shot wide again. Ronaldo appeared embarrassed. He looked to the sky and closed his eyes as the crowd's jeers rang around the Lviv Arena.
Ronaldo was the team's top scorer in qualifying for the tournament, racking up seven goals, but he's misfiring now. After the final whistle, while Pepe raised his arms and celebrated, Ronaldo crouched alone on the field, staring quietly at the turf.
"(Ronaldo) couldn't help us today with a goal," Pepe said, "but he helped to get us here today."
