With 11 minutes played, the 28-year-old then saw his chipped effort strike the inside of the post before rebounding to safety.
Despite having to withstand large amounts of pressure from the home side, Steve Bruce's Sunderland drew themselves level with their first meaningful shot on target. Former Arsenal midfielder Sebastian Larsson was the scorer, curling a free-kick beyond the reach of Wojciech Szczesny on the half-hour mark.
Szczesny would then come to his side's rescue four minutes later when he palmed away Lee Cattermole's header from close range.
The hosting Gunners had large spells of possession after the break, but very rarely forced a save from visiting goalkeeper Simon Mignolet.
However, after a free-kick had brought them level, Sunderland found themselves defeated by a goal scored via the same method. Captain Van Persie stepped up to bend his effort from the right-hand side of the area into the top corner of Mingolet's net.
The Black Cats thought that they had drawn level for the second time in the match through substitute Ji Dong-Won, but his effort was ruled out for offside.
Arsenal have moved up to tenth in the Premier League table with the victory.