The defending champion's 10th win in 11 rounds yesterday, provisionally lifted it four points clear of Atletico Bilbao and nine points above Real Madrid before they play matches later this week.
While Barcelona eased to another victory, crosstown rival Espanyol drew 0-0 at home with Malaga. The two Catalan clubs will meet on Friday in a city derby at Camp Nou.
Barcelona dominated early in Vigo and Alexis put the visitors ahead in the ninth minute when he pounced on the rebound of a shot by Fabregas after the former Arsenal star had stolen the ball deep in Celta's half.
After Celta had pushed forward in search of an equaliser late in the first half with Charles and Rafina, who is on loan from Barcelona, both going close, Fabregas put the game away three minutes after the restart.
With Celta again caught outnumbered after losing the ball, Messi drew in the defense and slipped the ball over for Fabregas to drill it under goalkeeper Yoel Rodriguez.
Messi laid the ball off again for Fabregas to unleash a shot that hit the crossbar and ricocheted off the outstretched Rodriguez before crossing the line in the 54th.