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The hosts started the game brightly, as Aspas latched on to a defensive mistake by the current La Liga champions and burst through on goal before firing the ball across the face of the net, squandering the first clear chance of the game.
However, after showcasing an energetic display from the get-go, it was the home side that took the lead as Nolito picked up an over-hit cross from Aspas, who then looped a curling effort into the far corner, high enough to put it out of Marc-Andre ter Stegen's reach.
Celta Vigo doubled their lead on the half-hour mark only minutes after breaking the deadlock, as Aspas broke through the Catalan defence to smartly chip the onrushing German keeper from outside the box to make it 2-0.
Luis Enrique's squad piled on the pressure as they looked to stage their comeback but found it difficult to break down the resilient Celta Vigo defence.