The hosts started really brightly and were able to keep the ball from their more illustrious opponents in the opening five minutes.
However, Barcelona got in behind following some poor defending, with Pedro's effort saved and Sanchez turning in the rebound.
Celta refused to let the goal affect their play and Nolito had an effort from the edge of the box deflected over the bar.
They were almost level just after the half-hour mark but Rafinha's skidding effort from just outside the box went narrowly wide.
The flow of the game was halted at the end of the half with a number of fouls from either side, but Barca were able to hold their lead into the break.