Barcelona missed first-choice goalkeeper Marc-Andre Ter Stegen, Gerard Pique and dropped Pierre-Emerick Aubameyang to the bench and started Ousmane Dembele.
The host desperately looked for a quick start after a rather passive opening and had Juanmi get past Dani Alves to direct a perfectly controlled angled ball wide of target.
A goalkeeping change then befell Manuel Pellegrini's men with 17 minutes played after Claudio Bravo limped to the touchline and was duly replaced by Rui Silva.
Barcelona were inches away from the breakthrough three minutes apart when Ronald Araujo headed a corner-kick from Memphis Depay off the woodwork and needed Silva to repel the rebound.
The Blaugrana should've trailed the host just inside the half-hour mark after a cutback on the edge of the area from Sergio Canales prompted Guido Rodriguez to slam against the post.
In a pretty cagey opening second half, the Catalans were closest to go in front when Dembele worked space from a long-kick by goalkeeper Neto and fired into the side-netting.
Neto was then called into action in the middle of the second period as he produced an expert save to parry Juanmi's close-range volley, whilst Aubameyang came on for Depay.
Barcelona made the breakthrough in the final 13 minutes after Ansu Fati brought a ball from Jordi Alba under control on the edge of the area and finished into the bottom-corner seconds after coming on.
The host weren't behind for long as former Barca defender Marc Batra got on the end of Nabil Fekir's delivery following a free-kick and headed past Neto from close-range.
Barca didn't lose momentum and got the winner with the last kick of the game after Alba volleyed a pin-point cross from Alves into the top corner to leave the host empty handed.