While the hosts matched their illustrious visitors in the first half, Barcelona romped away after the break as they won their 10th league game of 11.
Alexis Sanchez opened the scoring before an unfortunate Rodriguez Yoel own goal and a fierce strike by Cesc Fabregas guided Gerardo Martino's team to victory which means they have taken 31 from a possible 33 points this season.
Celta came into the match on the back of a stunning 5-0 win at Malaga, their first victory since August 25.
It snapped a winless run of seven games which had brought only two points and left them hovering around the relegation zone.
The hosts did well enough, taking the game to Barca but they found themselves a goal down inside nine minutes.
Gustavo Cabral wanted too much time on the ball and Fabregas pounced, dispossessing the defender and racing into the left side of the area.
He slid a shot across the keeper which Yoel parried but only into the path of Alexis and he emphatically tucked the ball away.
Alexis then had a header come off Yoel's ankle and away from goal as Barca threatened to cut through the home defence each time they attacked.
Alex Lopez's shot was blocked by Carles Puyol and Dias Charles forced Victor Valdes to dive full length to save his snap shot after the Barca defence was caught napping.
The visitors almost doubled their lead moments later when he twisted and turned in the Celta defence before floating a shot across goal and inches wide.
Celta went straight up the other end and were within a whisker of equalising when Alcantara Rafinha's shot from outside the area had Valdes beaten but the ball went inches wide.
The hosts were enjoying a good spell and Barca were grateful to Valdes when he blocked Rafinha's low drive from 12 yards out.
Celta did have the ball in the net after half an hour but the referee blew for a foul by Charles who stuck out a leg which tripped Valdes.
The second half was only two minutes old when Barca fortuitously doubled their lead.
There was some neat interchange between Dani Alves and Lionel Messi outside the area before the ball was laid off to Fabregas and the former Arsenal midfielder attempted to place his shot in the top right-hand corner.
The ball came off the bar and hit the back of Yoel, squeezing into the net before the keeper could claw it clear.
It was harsh on Celta who had gone toe to toe with the defending champions for the entire first half and an own goal was credited to Yoel.
However, there was nothing fortunate about the third goal six minutes later.
Messi powered forward, drawing the defenders to him and leaving Pedro and Fabregas unmarked.
He picked out Fabregas and the Spain midfielder ran on to the ball to fire a powerful shot inside the near post.
Yoel had to save with his feet from Messi and Barca were carving their hosts open at will.
Celta were not just going to go out with a whimper, Manuel Agido curling a free-kick against the bar with Valdes well beaten.
Pedro's shot clipped the bar and Messi brought out the best in Yoel with a flying save while Santi Mina's goalbound shot for Celta was blocked by Martin Montoya.