In the driving rain, the Danes scored three times inside 25 minutes with goals from Martin Jorgenson, Morten Wieghorst and Jon Dhal Tomasson, and a play-off place was theirs.
Ex-Newcastle striker Jon Dahl Tomasson has been in great form and Chelsea goalkeeper Ed De Goey's former understudy, Jerzy Dudek has been named as the most in-form keeper in the world on a Fifa list.