Portugal came close to scoring in the seventh minute, when Cristiano Ronaldo latched onto a through ball down the left, before moving past one defender, but his right-foot effort went slightly over the bar.
Four minutes later, Portugal produced more danger through a fast counter-attack that found Ronaldo without marking, but the Real Madrid ace's shot went straight at the keeper.
Denmark responded in the 16th minute as the ball luckily found the path of Jacobsen but the midfielder, with only the keeper to beat, could not direct it goalwards from close range.
In the 21st minute, the visitors wasted another chance. A low cross from Duda down the left found Simao, who did well to control the ball but his shot was weak and went straight into the hands of the keeper.
Portugal were dominating the game at this stage but were unable to capitalize on the many chances they were producing.
On 40 minutes, there were penalty claims by Portugal after Cristensen's hand ball inside the box but the referee waved away the protests. From the resulting corner, Simao Sabrosa tried his luck from 22 yards out but the effort went over the bar.
Just two minutes later, Denmark took the lead. A cross from the left found Bendtner in the box, and the Arsenal striker created space between Bruno Alves and Pepe to fire home a powerful shot with his left foot.
It was Denmark's first shot on goal but it was enough to give them the lead at half time. The Seleccao's wastefulness in front of goal was costing them.
The home side began the second period the brighter and could have doubled their lead on 56 minutes but Rommedhal's shot went just wide of the left post of Eduardo's goal.
Portugal wasted one of their best chances 63 minutes into the game, when Andersen could not save Raul Meireles' low cross from the left, Liedson could not score from close range and in the rebound Ronaldo's shot went against a Danish defender.
In the 87th minute, Portugal equalized through Liedson, who did not even have to jump to head home on his debut following a corner from the right.
The Seleccao would still try to find the winning goal on two occasions, without success. Denmark showed a lethal touch here, and demonstrated it's not the number of chances you create, it is what you do with the ball that counts, as they get closer to a place in South Africa.
Luís Mira, Goal.com
The 2010 World Cup is fast approaching, so keep up to date with all the news at Goal.com's World Cup homepage