A bright start for the Blue and Whites against Real Madrid and for a while they looked the far better side, but it was Real who opened the scoring after half an hour, Higuaín tapping in a sitter.
Cristiano Ronaldo made it 0-2 almost on the stroke of half time and added a penalty five minutes into the second half.
Stadsgaard got one back for Málaga but Higuaín then grabbed his second of the night to send Real Madrid to the top of the table and preserve their unbeaten start to the season.
The Blue and Whites played some impressive football at times but, unfortunately, failed to capitalise on a number of golden opportunities to score.
Barcelona fought back from a goal down to overcome Valencia 2-1. Pablo put the visitors ahead in the 38th minute but second half goals from Iniesta and Puyol gave the home side victory and they now go second in La Liga.