Luis Suarez scored a brace – both of his goals assisted by Lionel Messi – as Barca twice held the lead on the road on Saturday.
However, after Fedor Smolov had equalised earlier in the second half, Iago Aspas curled in an 88th-minute free-kick to bring Celta level again in a see-saw contest in Galicia.
The hosts missed a golden opportunity to snatch victory in the closing minutes too, Nolito shooting straight at Marc-Andre ter Stegen after being set up Denis Suarez.
5 - Barcelona have lost five points the last five minutes in @LaLigaEN games, more than any other team in the competition this season (level with Valencia). Slide#Celtabarcelona pic.twitter.com/YnYz0QGXU5— OptaJose (@OptaJose) June 27, 2020
While the result is good enough to move Barca a point clear at the summit, Madrid – who hold the head-to-head edge over their rivals – can retake top spot so long as they avoid defeat at Espanyol on Sunday.