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."
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.
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.
