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The 33-year-old Argentine superstar opened the scoring in the first half at the Camp Nou after a superb assist from Antoine Griezmann.
Griezmann cleared his marker with a superb spin before slotting the ball into the path of an onrushing Messi, who slammed the ball past Aaran Escandell with a fine finish.
But Barcelona's lead was undone in the second half as Darwin Machis and Jorge Molina scored to seal a sensational 2-1 win for Granada at the Camp Nou.
The Spanish club's defeat has left the La Liga title race wide open as Barcelona trail league leaders Atletico Madrid by two points.
Barcelona, who are third in La Liga, are level on points with fierce rivals Real Madrid with five matches remaining in the league.
Before Barcelona squandered their lead to Granada, Messi was presented with a fantastic opportunity to double his side's lead before half-time.
Messi managed to beat the Granada offside trap as the ball floated in from over the top and the Barcelona captain expertly controlled it with a brilliant touch.
The six-time Ballon d'Or winner was clean through and only had Escandell to beat, but the Granada shot-stopper closed down the angle.
Messi's shot clipped Escandell's foot as the Barcelona forward watched the ball roll out of play and out for a corner.
The Argentina captain's missed opportunity proved to be costly at the full-time whistle, but some fans have blamed Messi for essentially costing Barcelona the league title.
Barcelona will now return to action on Sunday when they travel to the Mestalla against Valencia.
Ronald Koeman's men will then welcome Atletico to the Camp Nou on 8th May for a crucial clash in the La Liga title race.
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