Barcelona are still looking for their first away win of the season after losing 1-0 to Rayo Vallecano on Wednesday night.
The pressure continues to mount on Ronald Koeman, with this result coming after Barça were beaten by Real Madrid in El Clasico at the weekend.
Rayo had the better of the opening exchanges, but the first chance fell Barça's way when Nico Gonzalez robbed Oscar Valentin of the ball, but Memphis Depay was unable to keep his opportunistic effort on target.
Nico then set Sergio Aguero through one on one with Stole Dimitrievski, but the Argentine tried to initiate contact with the goalkeeper to win a penalty and failed, with referee Antonio Mateu Lahoz telling him to get to his feet.
But it was Radamel Falcao who broke the deadlock after Sergio Busquets was robbed of possession in midfield by Oscar Trejo, and he fed the ball to El Tigre who found the far corner of Marc-Andre ter Stegen's net.
Barça had a golden opportunity to equalise before half-time when he met Depay's cross, but his close-range shot cleared the low roof of the stadium.
Nico had a great chance to level the scores just after half-time when Eric Garcia played a lovely floated ball into him, but his shot was wayward.
Barcelona continued to ramp up the pressure with Aguero twice going close, and they won a penalty 20 minutes from time when Depay was tripped by Valentin.
However, the Dutchman's penalty was well saved by Dimitrievski and Rayo remained in front.
Substitute Luuk de Jong had half a chance of earning a point in stoppage time when Dimitrievski rushed off his line to meet a loose ball but was too slow, and the Netherlands international tried to lob the North Macedonian but his shot went over.
Koeman threw Gerard Pique up front in frantic search of a goal and Aguero and Gavi spurned great chances to level it, but Rayo held on for their first win over Barcelona in nearly two decades.
FC BARCELONA PLAYER RATINGS
1. Goalkeeper & defenders
Marc-Andre ter Stegen (GK) - 5/10 - Not much he could do about the goal but didn't look assured on the ball either.
Sergi Roberto (RB) - 5/10 - Offered some support going forward but Rayo continually attacked his flank.
Gerard Pique (CB) - 6/10 - Wasn't his fault that Barcelona lost, that's for sure.
Eric Garcia (CB) - 6/10 - Comfortable on the ball but not to much off of it.
Jordi Alba (LB) - 5/10 - Audibly frustrated with how little of the ball he was seeing in the first half. Maybe Barça would have been better if they gave him the ball a bit more.
Sergio Busquets (CM) - 3/10 - Slow and ponderous, but now actually to the detriment of his team.
Nico Gonzalez (CM) - 8/10 - Barcelona's best player, full of energy and basically dd all of Busquets' work for him.
Philippe Coutinho (AM) - 5/10 - Flashes of flair but not enough to trouble Rayo thoroughly.
Sergino Dest (RW) - 4/10 - Just so obviously not a winger.
Sergio Aguero (CF) - 6/10 - Some decent sights of goal but he found a way to fluff them all.
Memphis Depay (LW) - 6/10 - Great at playmaking but good lord this man really cannot take on a defender or score a penalty.
Yusuf Demir (RW) - 4/10
Gavi (CM) - 5/10
Luuk de Jong (CF) - N/A