Memphis Depay missed a penalty as Barcelona lost at Rayo Vallecano to increase the pressure on Ronald Koeman.
Barca, defeated 2-1 at home to Real Madrid on Sunday, are ninth in La Liga.
Oscar Trejo won the ball from Sergio Busquets and fed veteran striker Radamel Falcao, who finished via the inside of the post for the only goal.
The visitors won a penalty when Oscar Valentin fouled Depay but his spot-kick was well saved by Stole Dimitrievski, who also smothered the rebound well.
It is the first time since September 1987 that Barca have lost three away games in a row without scoring – a run that saw English manager Terry Venables sacked.
Barca boss Koeman – whose car was surrounded by angry fans after losing El Clasico – admitted before this game his side “cannot afford back-to-back losses”.
Trejo, perhaps sensing Barcelona’s fragile mental state, tried to score from the halfway line in the third minute but his shot was saved by Marc-Andre ter Stegen.
Barca were uninspired yet again, with Depay’s penalty their only shot on target.
Luuk de Jong’s chip, Sergio Aguero’s header and Gavi’s scuffed shot were off target late on.
This is their fifth defeat of the season in all competitions and they sit six points behind leaders Sevilla and Real Sociedad.
Rayo – who have won all five home games this season – rise to fifth, above city rivals and champions Atletico Madrid.