The Catalans never relinquished control of the match or the tie, and could have racked up a double digit scoreline in an encounter they absolutely dominated
The Blaugrana were simply too good for their Segunda Division opponents, and progress by a 7-0 aggregate scoreline, setting up a date against Malaga in the last eight.
Thiago Alcantara opened the scoring 17 minutes in, before a pair of strikes of the highest quality from David Villa put the dominant hosts out of sight by half-time.
Alexis Sanchez would add two further goals in the second half, and Barca played out the rest of the match in complete control - without ever needing to call on Lionel Messi from the bench.
Stand-in coach Jordi Roura looked to rest a few of his first-team regulars, with Sergio Busquets and Jordi Alba joining Messi on the bench, as Villa was handed a start in attack.
Barca needed only two minutes to register their first chance of the match, as Sanchez was denied from close range by Mikel Saizar, who had to be alert minutes later to parry a curler from Cesc Fabregas on the edge of the area.
But Saizar could do nothing to stop Thiago in the 17th minute, as the midfielder was released by a deft touch from Alex Song, and bent a fine finish into the back of the net.
It should have been 2-0 within moments when Sanchez broke clear and attempted to lob Saizar, but the keeper stood his ground and was able to smother the effort.
But the second goal was always on the cards, and it arrived via a moment of brilliance from Villa. The striker collected the ball on the byline, slipped past two challenges effortlessly, and buried the finish.
The dust had barely settled before Villa struck again. Sergi Roberto’s nifty touch teed-up the Spain international on the edge of the area, and his shot was drilled in low via the post.
Thiago had a chance to make it 4-0 shortly after the half hour mark, but after taking aim superbly just outside the box, he was unlucky to see his shot ricochet off the woodwork.
Sanchez had another chance to score seven minutes into the second half, but after rounding Saizer, could not find the target with his finish. But the Chilean would come good almost instantly, rising highest to nod home Thiago’s corner from six yards out.
Vila then spurned a glorious chance to seal his hat-trick when he fired harmlessly over the bar from an unmarked position yards from goal, with Sanchez doing well to set up the chance.
It took Cordoba 66 minutes to register their first real chance, as substitute Pedro forced Jose Pinto into a close range parry after breaking free down the right.
But Barca responded as Jonathan dos Santos fired just wide from just outside the box, before Thiago came close again with a dipping shot that bounced onto the roof of the net.
With only minutes left, Sanchez lost his footing at point blank range after manoeuvring brilliantly to set himself up for a shot.
But he would not be daunted, bundling home a rebound moments later after Tello's shot was saved, to put the finishing touches on an enjoyable night for the hosts at Camp Nou.