The hosts opened the scoring three minutes before half-time when Arsenal striker Nicklas Bendtner controlled a high ball from Michael Silberbauer in the middle of the penalty area and blasted it into the top right corner.
Portugal had many chances to score but Denmark goalkeeper Stephan Andersen made one save after another until Brazilian-born striker Liedson finally headed the ball in from inside the penalty area to equalise with four minutes to go.
"Generally speaking, Portugal were the better team," Portugal coach Carlos Queiroz said. "We had more chances ... We created chance after chance, but didn't score.
"That's the main difference tonight. Bendtner had one chance and did what we couldn't do with 50," he told a news conference.
Portugal were the more aggressive side in the second half and in the 68th minute Simao Sabrosa found Tiago on the left but the midfielder's shot went wide.
A few minutes later, Portugal captain Cristiano Ronaldo sent his 30-metre free kick just over the crossbar, while playmaker Deco also went too high with a free kick in the 80th minute.
Denmark, bidding for a return to the World Cup after missing out in 2006, top the group with 17 points from seven matches, four ahead of second-placed Hungary who lost 2-1 at home to third-placed Sweden, who have 12 points. Portugal are fourth with 10.
Denmark coach Morten Olsen said he was "both satisfied and disappointed" with the draw, which kept his team undefeated in the group and extended their lead over Hungary.
"Now we need to regain power before (the qualifier away to) Albania on Wednesday. There were many good individual performances," Olsen said.
