The hosts started brightly and were able to keep the ball from their more illustrious opponents in the opening five minutes.
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.
Five minutes later the game was over as a contest and it was Fabregas again, who drove into the box and rifled a shot into the bottom corner.
Former Barca striker Nolito almost got the goal he deserved but saw a free kick come back off the bar.
Lionel Messi squandered two late chances and there were no further goals with Barca taking the points comfortably.