The Catalan giants came into the clash at Balaidos having seen bitter rivals Real Madrid cut their lead at the top of the table to one point with a 9-1 demolition of Granada.
Celta had beaten Barca 1-0 in the reverse fixture back in November, but this time it was Luis Enrique who got the better of his former club as Jeremy Mathieu nodded in Xavi's free-kick in the 73rd minute.
It was a crucial goal on the back of a less-than impressive Barca performance, but the coach praised his players for grinding out the victory.
"It has cost a lot," he said. "We believe that they are important points because of the difficulty [of the game].
"To win this way reinforces the squad and prepares us for what's left."
Matchwinner Mathieu added: "It was a difficult game, but sometimes matches are won with small details.
"Sometimes you have to suffer, but the three points are the most important thing."
