Two goals from the Brazilian either side of the Argentine to give the hosts all three points, although Victor Valdes' potential season-ending injury overshadowed proceedings
The Spain goalkeeper is set to leave the club at the end of the season and, if the injury to his right knee - sustained while making a simple save - proves serious, he may have played his last game in a Barcelona shirt.
There was a further worry for coach Gerardo Martino when Andres Iniesta was withdrawn at half-time as a precaution with a niggling thigh problem.
Yet, three days after Sunday's epic Clasico victory, a routine win at Camp Nou at least allowed Barca to apply further pressure to La Liga title rivals Atletico and Real Madrid.
Two goals from Neymar and one from Lionel Messi proved enough to see off a Celta side coached by Barca legend Luis Enrique.
The visitors threatened sporadically, most notably just after half-time when Valdes' replacement Jose Pinto made an excellent double save to deny Augusto Fernandez and Santi Mina.
Celta were already two down by that stage, however, Neymar having finished off a trademark flowing move from Barca with a simple tap-in, before Messi ran on to Iniesta's pass and beat goalkeeper Yoel for his 22nd league goal of the season.
Neymar, who had come in for criticism following his performance against Real, added his second and Barcelona's third in the 67th minute, allowing the Catalan giants to celebrate their 1,000th La Liga match at Camp Nou in style.
Neymar's opener came inside six minutes as he tapped into an empty net after incisive approach play involving Iniesta, Messi and Alexis Sanchez.
The Brazilian ought to have doubled his tally nine minutes later, firing into the side netting from a tight angle after being picked out by Messi, who was then denied by Yoel after breaking in behind the Celta backline once again.
The hosts suffered a setback midway through the half when Valdes had to be carried off on a stretcher.
Adriano was penalised for handball close to the edge of the area and, after appearing to originally award a penalty, referee Miguel Ayza gave a free kick, from which the keeper fell awkwardly on his right knee while making a routine save.
Despite a lengthy stoppage, Barca's rhythm was not disrupted as Messi doubled the advantage on the half-hour, latching on to Iniesta's pinpoint pass before rounding Yoel and slotting in.
Seven minutes into the second half, Pinto made a superb double stop, first keeping out Fernandez's close-range prod before jumping to his feet to parry away Mina's powerful rebound.
Neymar then put the result beyond doubt, picking up Sanchez's raking pass before firing beyond Yoel low into the bottom right-hand corner.
Sanchez shot wide 18 minutes from time after being picked out by substitute Pedro but it mattered little as Barca comfortably saw out the victory.