The goalkeepers were the heroes of the night. Denmark's Thomas Sörenson repeatedly denied Zlatan Ibrahimovic and Johan Elmander, who dispelled the notion that they are incompatible in the Swedish forward line.
Sweden dominated the first half and Ibrahimovic was at the heart of it, dazzling early on with a fierce volley after controlling the ball on his chest and juggling it a couple of times before unleashing his shot direct at Sörenson.
Elmander was lively too, forcing Daniel Agger into a foul after 20 minutes which prompted the second yellow card of the game. Denmark's Daniel Jensen picked up the first yellow on 8 minutes after he brought down Christian Wilhelmsson.
Zlatan Ibrahimovic will rue the 80th minute punch that led to his booking - the yellow card means he will be suspended for Sweden's next match.
With Sweden's 21 shots on goal to Denmark's 12, coach Lars Lagerbäck felt that his team deserved more than one point from the game.
"Sörensen made a couple of amazing saves," he said after the game.
"We're in a good position to qualify."
Sweden's next Euro 2008 qualifying match is away to Liechtenstein on October 13th.