Barcelona dominated possession with wonderful passing, working tirelessly to harass the home side in their short spells on the ball, and deservedly led through a David Villa goal after 26 minutes.
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That would have been kind on Arsenal, beaten 6-3 on aggregate by the Spaniards in last season's quarter-finals, but they got a huge bonus seven minutes from time when substitute Andrei Arshavin swept in the second after a superb counter-attack.
"They are the best side in football's history in my opinion. That is one game and this is half-time," Arsenal captain Cesc Fabregas told ITV Sport.
"It is a nice victory but that's all. If we show it here and not the Camp Nou, it is nothing for us."
Dutchman Van Persie, who missed both matches in last year's quarter-final, said Arsenal had beaten Barcelona at their own game.
"In our opinion if you drop back too much they are so good they will beat you," he said. "We had to beat them in their own style. It was a fantastic result in the end."
Messi ran on to the first from Villa after 15 minutes but though the striker's dummy took Arsenal keeper Wojciech Szczesny out of the equation his dinked finish rolled inches wide.
