The France full-back, who extended his contract with the Spanish and European champions on Monday, galloped on to a floated Lionel Messi pass 13 minutes from time and calmly slotted past Iker Casillas to give the 2011 runners-up the advantage for next week's second leg in Barcelona.
Real forward Cristiano Ronaldo had put the home side ahead with a breakaway goal in the 11th minute before Barca captain Carles Puyol flung himself at Xavi's corner to power a header past Spain team-mate Casillas for a 49th-minute equaliser.
"We won this game but we have to be careful in the return match because that's going to be another tough test," Abidal, whose goal was only the fourth of his career, said in a television interview.
"I seem to be a cup player," the 32-year-old former Olympique Lyon player added. "I scored in the cup back in France and I seem to be doing it again in Spain."
The winners of the tie will face Valencia or their city neighbours Levante, who play their quarter-final first leg on Thursday.
On the other side of the draw, headers from the towering Fernando Llorente and the diminutive Iker Muniain gave Athletic Bilbao a 2-0 win at home to Real Mallorca in their last-eight first leg earlier on Wednesday.
If the Basques can hold on in Mallorca next week they will play 2006 champions Espanyol or third-tier Mirandes, who are through to the quarters for the first time.
Mirandes stunned Espanyol by opening a two-goal lead in their first leg on Tuesday before the home side struck three times in four minutes late on to secure a 3-2 lead for the second leg in Miranda de Ebro.
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Real coach Jose Mourinho sprung a couple of surprises in his starting line-up for the fourth of a possible eight meetings between Real and Barca this season.
He included Portuguese compatriot Ricardo Carvalho in central defence despite the Portugal international not having played for several months due to injury.
He also deployed Hamit Altintop at right-back, handing the Turkey international only his third start of the season, and moved centre-back Pepe forward into midfield to try to thwart Barca's approach play.
The match quickly settled into a pattern familiar from recent meetings, with Barca dominating possession and Real looking to use the pace of Ronaldo, Karim Benzema and Gonzalo Higuain on the break.
After Ronaldo's opener, when Barca goalkeeper Jose Manuel Pinto let the ball under his body, Casillas produced smart saves to deny Messi and Andres Iniesta while Alexis Sanchez sent a looping header onto a post from a Cesc Fabregas cross.
Pepe, who had earlier been booked, was lucky to stay on the pitch in the second half after television replays showed he deliberately stamped on Messi's hand when the World Player of the Year was sitting on the ground.
There were a few ugly challenges late in the game and Carvalh
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