Gerard Pique's first-ever double for Barcelona went in vain as rampant Celta Vigo snatched a 4-3 victory over the Spanish Giants in their chaotic La Liga clash here at Balaidos on 3 October.
Barcelona had a chance to surge to the top of the standings after Real Madrid drew 1-1 at home to minnows Eibar, but they instead slumped to their second defeat of the season.
Midfielder Pione Sisto opened the account for Celta in the 22nd minute before striker Iago Aspas doubled the lead for his side just nine minutes later, goal.com reported.
In the 33nd minute, Barcelona was hit again when Jeremy Mathieu smashed a goal into his own net to pile further misery on his side.
Luis Enrique's side launched a comeback after the break, with Gerard Pique scoring a header in the 58th minute before Neymar pulling one back for his side just six minutes later.
However, a blunder from Barcelona goalkeeper Marc-Andre ter Stegen helped Pablo Hernandez clinch a match-winning header for Celta in the 77th minute.
Although Pique reduced the deficit to a single goal just few minutes before the final whistle, it was not enough to undo the damage done by Barcelona's shaky defence.
With the defeat, Barcelona have now dropped to fourth place in the standings, two points behind leaders Atletico Madrid and Real.
The Enrique-led side will next lock horns with Deportivo on October 15.