Kosovar Asllani, who missed the last league match when she operated on her left thumb, had several of the best goal chances in the first half.
But it was the team's second Swede, Sofia Jakobsson, who scored the first goal of the match.
Placed a good distance outside the goal area, she sent in 1-0 on a volley in the 43rd minute.
Real Madrid is currently third in the Primera Division.
The match is in progress.
ARCHIVE: Here both Jakobsson and Asllani net for Real Madrid 4 November 2020
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Double Swedish goals for Read Madrid - Jakobsson and Asllani hit Photo: Real Madrid