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Madrid welcomed back Falcao to the starting lineup but fell behind after four minutes when Alhassane Bangoura burst into the box unmarked before smashing into the top corner from a tight angle for his third goal of the season.
Things got worse for the visitors before the break as Bangoura crossed for Leo Bauptista to turn home from close range.
Falcao cut a frustrated figure in attack as Rayo continued to threaten on the break, with Pitti impressing with a series of incisive forward bursts.
The Colombian striker netted a consolation in stoppage time but Rayo held on to secure three points that move the in-form side into a European place.