Barcelona hold on to eliminate holders Real
After Barca won last week's first leg in Madrid 2-1, Real came out swinging and probably had the better of the opening exchanges before Lionel Messi released substitute Pedro to open the scoring for the home side in the 43rd minute in front of almost 100,000 spectators at a raucous Nou Camp.
Full-back Daniel Alves looked to have settled the tie when he blasted a spectacular second in first-half added-time, running on to a loose ball and sending a thunderous drive past Real goalkeeper Iker Casillas into the top corner.
Barca appeared to be in total control and they dominated possession at the start of the second half but Real rallied and mounted a rousing late fightback that left them needing just one more goal to advance.
Cristiano Ronaldo, who scored the extra-time winner when Real beat Barca 1-0 in last year's cup final, sped on to Mesut Ozil's pass and finished past Jose Manuel Pinto just over 20 minutes from time and Barca were reeling when substitute Karim Benzema levelled four minutes later.
Both sides had chances in the frenetic final stages before Real centre-back Sergio Ramos was sent off for a second yellow card and Barca then ran down the clock to set up a semi-final against Valencia or Levante, who meet on Thursday.
"The players played a good game," a subdued Real boss Jose Mourinho told a news conference full of curt answers.
Real had played well in the first half and did not deserve to be two behind at the break, he said, adding that he had told his players he wanted more of the same in the second period.
"Before the game we came here with the hope and the motivation of winning," he said.
"If you want I will congratulate Barcelona for the win last week. I am happy to do that as they deserved to win."
The build-up to the game, the fifth meeting between the pair this season, had been dominated by the controversy over an alleged stamp on Messi's hand by Real defender Pepe.
Mourinho included his Portuguese compatriot, who said he did not mean to tread on Messi, in the starting line-up and his every touch was greeted with howls of derision by the Barca faithful.
Barca almost fell behind seconds into the game when centre-back Gerard Pique inexplicably let the ball run through to Gonzalo Higuain but the Real striker skewed his shot wide.
Both sides were on the attack from the start and Ronaldo tested Pinto with a powerful low drive before Messi curled a shot narrowly wide after a swift break orchestrated by Cesc Fabregas.
Ozil came within a whisker of putting Real ahead in the 25th minute when he tried a shot from distance that shook the crossbar and bounced down just outside the goal-line.
Pinto, who plays in the cup instead of first-choice goalkeeper Victor Valdes, then played the ball straight to Higuain but again the Argentina international was unable to take advantage of the error.
An attritional second half was full of controversial moments, with a slew of fouls and yellow cards leaving the Real players furiously berating the officials as they exited the pitch.
Barca's success extended coach Pep Guardiola's recent dominance over Real. He has won nine 'Clasicos' and only lost once, in the 2011 cup final, in 14 games since taking charge in 2008.
Mourinho, by contrast, has yet to find the formula that will help Real end Barca's Spanish and European dominance, although his side are five points clear of the champions in La Liga with half the season played.
"It's more difficult each time to beat Real Madrid and that's why we are pleased with the game today," Guardiola told a news conference.
"Madrid are a great team and that's why the victory is worth so much," the former Barca and Spain midfielder added.
"They played a good match but over the 180 minutes we were the deserved winners."
Barca full-back Alves, who blasted a spectacular goal to make it 2-0 in first-half added-time, said Real had played "phenomenally well."
"This is the version of Real Madrid that causes us the most problems because they pressure you a lot," the Brazilian said.
"They were closing us down well and making it difficult for us to bring the ball forward.
"But the important thing is that we have the victory in the tie in the bag."
On the other side of the draw, Athletic Bilbao set up a last-four clash against third-tier Mirandes when a howler by home goalkeeper Juan Jesus Calatayud gifted them a 1-0 win at Real Mallorca for a 3-0 aggregate success.
After last week's first leg at the San Mames ended 2-0 to the Basques, time was already running out for Mallorca when Ivan Ramis played an innocuous-looking pass back to Calatayud in the 76th minute at the Iberostar stadium.
As the goalkeeper prepared to control the ball, it popped up off the turf and rolled past him into the net to end the Balearic Islands club's hopes of repeating their 2003 cup triumph.
Their misery was completed when defender Chico was sent off late on and he clashed with his coach Joaquin Caparros, who had a stint in charge at Bilbao, and punched the dugout in frustration as he left the pitch.
Tiny Mirandes pulled off a huge upset on Tuesday when a goal in added-time gave them a 2-1 win at home to Espanyol that sent them through on away goals, only the second time a team from the third level has reached the last four.