Sjoeke Nuesken and Guro Reiten gave Chelsea the lead before Alba Redondo pulled one back for the visitors before half-time.
Mayra Ramirez struck in the second half to restore Chelsea’s two-goal advantage. A late Linda Caicedo tap-in set up a nervy finale at Stamford Bridge.
Chelsea went into the lead in the second minute when Johanna Rytting Kaneryd’s cross struck the unfortunate Sheila Garcia, via the head of Nuesken, and trickled into the Madrid net.
The English champions doubled their lead shortly before the half-hour as the referee pointed to the spot after Maria Mendez caught Nuesken as the pair fought over a loose ball in the box.
Reiten slotted the spot-kick beyond the reach of Misa Rodriguez, who had correctly guessed which way to dive.
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