The Dutchman struck in the 78th minute to cancel out David Villa’s opener before Andrei Arshavin secured the win with seven minutes remaining.
And van Persie was delighted his side won by playing their natural game against a brilliant Barca outfit, which at times opened up the Gunners vulnerable defence.
"Just to play our own game,” van Persie told ITV1 about the Gunners’ game plan.
"In my opinion, and in our opinion, if you drop back too much they are so good they will in the end beat you by far.
"We had to beat them in their own style.
"We got a bit lucky but it was a fantastic win."