Messi played a pivotal role in Ousmane Dembele opening the scoring against the Galicians in the 10th minute, firing a shot at goal which Celta's Ruben Blanco could only parry at the feet of the French forward, who squeezed the rebound through the goalkeeper's legs.
The Argentine then scored a sixth goal in three La Liga games to stretch his side's advantage on the stroke of halftime, latching onto a pass from Jordi Alba and producing an irresistible finish beyond Blanco just as he entered the area.
Celta had conceded 18 goals in their previous four visits to the Nou Camp and although they fared better in defence this time, they struggled to cause Barca many problems, particularly after Spain international and top scorer Iago Aspas went off injured early in the second half.
Barca lead the standings on 37 points, three ahead of second-placed Atletico Madrid and six clear of Sevilla who play against Leganes on Sunday.
Real Madrid, who were crowned Club World Cup champions on Saturday by beating Al Ain 4-1, are eight points back from Barca in fourth place but with a game in hand.
(Reporting by Richard Martin; editing by Martyn Herman)
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