Instead, it was another Swede who got to celebrate.
Fridolina Rolfö started for Barcelona and played 72 minutes for the guests.
There does not seem to be anything that can stop the sovereigns of Catalonia.
The reigning Champions League champions have won all matches this season.
Barcelona decided quickly
And in the classic meeting with Real Madrid, the team pressed the gas immediately.
After just 23 minutes, Barcelona led 3-0 after double goals by the Dutch Lieke Martens and a full hit by Irene Paredes.
Asllani gave the home team some hope when she reduced in the beginning of the second half, but no closer than that came Real Madrid.
Barcelona undefeated
This is the second match in a row that the Swedish national team player enters the goal record.
In the Champions League match against Icelandic Breidablik on Wednesday, she became a two-goal shooter.
Barcelona have 13 wins in as many matches in La Liga so far.
Real Madrid, on the other hand, has had a much heavier start to the season and is in tenth place, with 17 recorded points.