It was a disappointing night for Barca whose fans showed up at an almost sold-out stadium to see their new team headlined by Poland striker Lewandowski, the twice FIFA Best Player of the Year winner, and Brazil winger Raphinha.
Barcelona dominated the match with almost 70% of possession and 18 goal attempts to two for Rayo.
But the two best chances fell to the visitors, Alvaro Garcia thwarted by a brilliant save by Marc Andre ter Stegen and Sergio Camello shooting wide.
As the frustration mounted for Barca, their captain Sergio Busquets lost his cool and was sent off for an elbow to the face of Falcao Garcia in stoppage time.