Barcelona's title hopes suffered a setback as they were beaten 2-1 at Deportivo La Coruna in La Liga on Sunday.
Luis Enrique made five changes from the dramatic midweek Champions League win over Paris Saint-Germain, with Neymar ruled out, and Barcelona lacked a cutting edge at Riazor.
On-loan Stoke forward Joselu gave Deportivo the lead in the 40th minute, only for Luis Suarez to level shortly after half-time.
But as Barca struggled to create further opportunities, Alex Bergantinos headed in the winner for the hosts from a corner in the 74th minute.
Barca are now two points behind Real Madrid in La Liga after Los Blancos beat Real Betis 2-1 later on Sunday evening.
The win lifts Deportivo up to 15th in the table and keeps them unbeaten under manager Pepe Mel, who took charge at the end of February.
Having produced the greatest comeback in Champions League history on Wednesday, Luis Enrique opted to make several changes, with Neymar and Rafinha both out injured and Andres Iniesta, Samuel Umtiti and Ivan Rakitic dropping to the bench.
Arda Turan, Denis Suarez and Andre Gomes were among those who started, but despite the fresh legs, Barca still struggled to get going in the first half.
The hosts were compact in defence and had the first shot on goal as Joselu fired at Marc-Andre ter Stegen from outside the box.
Barca enjoyed plenty of possession but it took them until the half-hour mark to really threaten as Suarez headed at German Lux from the penalty spot and then Gomes curled a shot over.
Ter Stegen pulled off a good save to deny Joselu, but moments later he was beaten by the on-loan Stoke forward, who finished from a corner after Barca failed to clear.
Although Depor maintained their lead until half-time, Barca started on the front foot in the second half and soon levelled, with Suarez firing into the bottom corner from 12 yards.
But the visitors could not build any momentum and it was Depor who went close as Faycal Fajr shot over and Joselu volleyed at Ter Stegen.
Messi, who was subdued throughout, hit a first-time effort off target, but it was the hosts who scored next as Bergantinos climbed above Jordi Alba at a corner to head home.
Barcelona pressed in the final 15 minutes without any reward as Suarez saw an effort saved and Sergi Roberto, who scored the decisive sixth goal against PSG, volleyed over.
Deportivo should have added a third in injury-time when they broke clear, but Faycal's miss did not prove costly as the final whistle went shortly afterwards.