Lionel Messi, fresh from breaking Gerd Muller's record for goals in a calender year, was the difference once again for the defending champions, scoring in either half to take his 2012 tally to 88 goals and put his side in pole position to advance to the quarter-finals ahead of their Segunda Division opponents.
The Argentine opened the scoring 11 minutes into the game with a tap-in from close range and rounded off the win with his second goal 16 minutes from full-time to end the resistance of Cordoba, who will be disappointed in the result after fashioning many chances in a fine attacking display.
Victor Valdes, Cesc Fabregas and Andres Iniesta did not make the trip to Andalusia, as Jose Pinto, Thiago and Alex Song were chosen to start in their stead.
All the early momentum belonged to Cordoba, with a powerful drive from Fede forcing Pinto into an acrobatic save, before Sebastian Dubarbier crossed towards the far post, where Pedro Antonio drilled just wide.
But Barca would survive the early test of their character, and began to hit back at the other end of the pitch. Thiago crashed a 20-yard half volley off the frame of the goal, and with 11 minutes gone, the Catalans would make the breakthrough.
With the Cordoba defence surrounding him, Pedro showed good awareness to pick out the unmarked David Villa on the left, who had ample time and space to square to the equally unmarked Messi for a tap-in from a few yards out.
The hosts thought they had equalised within minutes of the restart, but after Fede’s excellent cross was turned home by Vincenzo Renella, the linesman flagged for a narrow offside to chalk off the effort.
Though Cordoba still harboured the potential to threaten the Barca defence, the match began to settle into a more measured tempo as the Blaugrana began to string a few impressive sequences of possession in midfield.
The home side saw another opportunity go begging two minutes into the second half, as Carlos Caballero took aim from the edge of the area, only to see Pinto make the save at his post.
Barca themselves then wasted two chances to extend their lead, with Pedro first volleying just over the bar from close range, before Villa sidefooted off target after being played into space.
Pedro had another opening soon after, when a well-worked sequence from Messi and Xavi saw him teed up inside the area, but Mikel Saizar was alert to make a timely stop.
The attacking momentum displayed by Cordoba in the first half was nowhere to be found, as Barca were able to control possession and play through the middle in their usual manner.
With 20 minutes to go, Messi seemed set to put the match beyond doubt after latching onto a brilliant through pass from Gerard Pique, but after being put in the clear, he could not beat the onrushing Saizar with his finish.
But Messi would make no such mistake four minutes later, as he sprinted in unmarked at the far post to slide home an incisive cross from substitute Alexis Sanchez to put the Catalans two goals ahead.
Saizar was called into action again late on to deny the Argentine his hat-trick, but Barca had already done enough to seal the win, and will take two away goals into the second leg at Camp Nou on January 10.