Barcelona had teenagers Pedri and Gavi to thank after returning to the top of the table ahead of next weekend’s trip to the Santiago Bernabeu to face Real Madrid.
Xavi had to prepare his squad for the contest while coping with a long list of injury absentees, including the likes of Franck Kessie, Andreas Christensen, Ronald Araujo and Hector Bellerin.
Despite the loss of some key men, Barca took an early lead when Gavi teed up Pedri to open the scoring in the 17th minute.
Barcelona were dominant in the first 45 minutes and were good value for their half-time lead but Celta came roaring back after the break and had chances to equalise.
Strand Larsen did get the ball in the back of the net for the visitors but Barcelona escaped when it was ruled out for an offside in the build-up.
Goalkeeper Marc-Andre ter Stegen then saved from Iago Aspas in the closing stages as Barca hung on to three vital points that will see them arrive at the Santiago Bernabeu on October 16 above Real Madrid in the table.