In their previous 18 fixtures, Barcelona had scored 66 goals and conceded just seven and it was quite the turnaround for Real Madrid who, just two months ago, were thrashed 5-0 in the Supercopa de Espana by the same opposition.
Moller was handed a rare chance in the starting lineup and she showed her gratitude by providing a wonderful assist for Real Madrid's opening goal after 41 minutes when she produced a pinpoint delivery for Alba Redondo to head the ball into the net above the reach of Cata Coll.
Norwegian international Caroline Graham Hansen restored parity for Barca in the 67th minute before Scottish striker Caroline Weir fired the visitors ahead in the 87th minute and struck again in stoppage time to round off a famous win for the visitors.
"It's special," Madrid's Redondo told DAZN after the match. "Clasicos are Clasicos, there was a nice atmosphere, playing at a place like Montjuic... we will keep evolving.
"We always believed (we could beat them), we have a big squad, they have a lot of quality to be at the top, but we believe we can win all games.
"Today is a party because it's the first time (we've done it)."
The win was a significant boost for Ream Madrid before their visit to Arsenal in the women's Champions League on Wednesday where they hold a 2-0 advantage from the quarter-final first leg, while Barcelona will pay host to Wolfsburg on Thursday with a 4-1 lead.