Albion are level with the former Champions League finalists after Glenn Murray equalised from the spot with a 38th minute penalty.
The Spanish visitors went ahead from a Rodrigo strike that appeared to have been helped by a sizeable deflection from Lewis Dunk.
Both Leandro Trossard and Martin Montoya have looked useful for the Albion.
For reference 10 years ago this weekend Brighton and Hove Albion were playing a pre-season friendly against Scunthorpe United.
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