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Barca entered the game on a three-match winless run in all competitions, having been held by Granada after a last-gasp equaliser before consecutive cup defeats after extra-time.
The stage was set for another frenzied finish after Luuk de Jong passed up two presentable opportunities for the Blaugrana, and it was his namesake who delivered this time.
Xavi's men leapfrogged Real Sociedad into fifth place in the LaLiga table, a point behind Atletico Madrid after its own late show a day earlier.