Barcelona, who suffered their first La Liga defeat of the campaign last weekend, saw off a battling Malaga in their quarter-final second leg tie after the two sides had been locked 2-2 from the first meeting.
Defending champions Barcelona went ahead on the night after just nine minutes when Pedro Rodriguez headed in a cross from Dani Alves after good work by Xavi.
But Joaquin Sanchez, with a right-foot drive, levelled for Malaga three minutes later.
Four minutes after the interval, Gerard Pique, who became a father for the first time this week when pop star girlfriend Shakira gave birth to a son, marked the occasion by volleying in Barcelona's second.
Roque Santa Cruz controversially equalised in the 68th minute after a Malaga counter-attack.
But Barcelona were furious that Cesc Fabregas had not been awarded a penalty when he was stamped on by Wellington.
Eight minutes later Andres Iniesta made it 3-2 after a smart one-two with Fabregas before Lionel Messi grabbed Barcelona's fourth of the night, heading in an 80th-minute cross from Iniesta for a 6-4 aggregate.
In the night's other tie, Atletico Madrid drew 1-1 at Real Betis for a 3-1 aggregate and a semi-final clash against Sevilla.
Real Madrid advanced to the semi-finals on Wednesday after a 1-1 draw at Valencia saw Jose Mourinho's side progress 3-1 on aggregate.
Leading 2-0 from the first leg in Madrid, Karim Benzema gave Real the lead a minute before half-time but Tino Costa levelled for the home side on 52 minutes following Fabio Coentrao's dismissal.
Real also saw Angel di Maria dismissed late on.
Sevilla clinched their berth in the last four with a 4-0 rout of Real Zaragoza following a goalless first leg.
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