The Primera Liga leaders will face city rivals Espanyol in the last eight, Sevilla play Valencia, Real Mallorca take on Real Betis and Sporting Gijon will face either Athletic Bilbao or Osasuna, who play their second leg on Thursday.
Atletico sparked hopes of an unlikely comeback from their 3-1 defeat in last week's first leg in Madrid when striker Florent Sinama Pongolle headed them in front on 24 minutes.
But their chances were effectively snuffed out only a minute later when Krkic leapt to nod Silvinho's cross into the top corner past Gregory Coupet.
Atletico's woes were compounded when Sergio Aguero had to be replaced midway through the second half with the Argentine striker in some discomfort from what appeared to be leg cramps.
Barca made sure of progress soon after when Gudjohnsen drove the ball into the net after good work from Andres Iniesta down the left, condemning the visitors to a fourth straight defeat in all competitions.
Luis Fabiano (pictured) scored twice for Sevilla as the 2007 Cup winners brushed Deportivo Coruna aside 3-0 to run out 5-1 winners on aggregate.
But holders Valencia needed extra time to see off Racing Santander 3-1, two goals from Vicente and one from Joaquin sending them through to the last eight 4-2 on aggregate after both the first leg and the opening 90 minutes had ended 1-1.
CALAMITOUS ERRORS
Sevilla took the lead at Deportivo in the opening minute when Jesus Navas volleyed home a cross from winger Diego Capel.
A couple of calamitous Depor defensive errors then gifted Luis Fabiano two goals to leave Sevilla 3-0 up at halftime.
The Brazilian robbed defender Diego Colotto and rounded goalkeeper Fabricio for his first with just over 20 minutes gone and then a collision between Colotto and Adrian Lopez let him in to score a second just before the break.
Sevilla finished the match with 10 men after keeper Andres Palop was sent off for felling Colotto in the area with around five minutes left.
Sevilla's Uruguayan striker Ernesto Chevanton, just back from injury, pulled on the keeper's shirt and watched Pablo Alvarez skew his shot off the post and wide.
In Valencia, Gonzalo Colsa equalised for Racing in the 21st minute, shortly after Vicente had given the home side the lead from the penalty spot, but neither side was able to find a winner in regular time.
Oriol Lozano's misplaced backpass in the first period of extra time allowed Vicente to run through and lift the ball over Tono for Valencia's second and Joaquin sealed the win with a superb finish to a swift break.
In other second legs, Segunda B (third tier) teams Poli Ejido and Real Union were eliminated by Espanyol and Real Betis respectively, although Espanyol needed the away goals rule to progress after Wednesday's tie ended 3-3 on aggregate.
Jorge Garcia's header in added time sent Sporting
