The African Footballer of the Year scored in the 37th and 56th minutes to secure Barcelona’s consecutive victory in all competitions.
The win increased Barcelona’s tally to 40 points in first place, five points ahead of second-placed Osasuna who play Atletico Madrid at home on Thursday.
Barcelona’s lethal duo Ronaldinho and Eto’o showcased their FIFA Player of the Year and second runner-up trophies ahead of the game.
Celta could have taken the lead twice at the start of the game but Brazilian striker Fernando Baiano saw his efforts denied once by the woodwork and the other by Barca keeper Victor Valdes.
Barcelona soon took control of the situation and snatched the lead when Ronaldinho took a free-kick while Celta players disputed the decision.
The Brazilian passed the ball to Eto’o who chipped it home past advancing Celta keeper Esteban from a tight angle.
Andres Iniesta brilliantly set-up Barca’s second when he picked out Eto’o with a deft pass through a forest of Celta players.
The Cameroon international had no problem firing into the corner of Esteban’s net.
Primera Liga action continues on Wednesday and Thursday before entering the winter break.