Arsenal went ahead with less than 30 seconds on the clock when Gervinho surged down the left and crossed for the inspirational Van Persie who shot into the bottom corner.
The hosts then dominated with a confidence they have struggled to find this season before letting Sunderland into the game when Mikel Arteta conceded a free kick that Seb Larsson struck beautifully over the wall to equalise against his former club on 31 minutes.
Arsenal had goalkeeper Wojciech Szczesny to thank when his point-blank save denied an unmarked Lee Cattermole shortly before halftime and they had to wait until eight minutes from time for Van Persie to snatch the victory.
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The Dutchman more than matched the quality of Larsson's free kick with one of his own that curled over the wall and into the goal to lift Arsenal up to 10th in the league with only their third victory in eight games.
"We had a good start for 25 minutes but as soon as Sunderland equalised the confidence started to wobble a bit," Wenger told Sky Sports.
"The second half was all us ... but we needed something special from Robin van Persie to make the difference ... When you need something special in game that's where you see great players and that's what you saw today.
"What matters for us at the moment is the three points. (Confidence) comes back with points. The spirit is great in the team."
Van Persie had also hit the post in the 12th minute and was lively throughout, making his reassurance in his programme notes that he was committed to the club despite an impending house sale very welcome reading to fans.
"It was my first touch of the ball so I was a bit surprised," Van Persie told Sky Sports when asked about his opener. "But it was a really good pass from Gervinho, I took a good touch with my left foot and it went in."
TOO GOOD
The striker added it had been worth getting a yellow card for taking his shirt off to celebrate the winner.
"I just felt confident, it was my favourite position, it's been a while ... I have missed many in the last couple of months," he said. "It was about time to be honest."
Defeat leaves Sunderland just above the relegation zone in 17th and turns up the heat on already under-fire manager Steve Bruce.
"We'll stick with it and we'll turn it around," Bruce said. "We've had a disappointing start, we can't disguise that."
Earlier in the day, West Bromwich Albion claimed the Midlands bragging rights with a 2-0 win at home to Wolverhampton Wanderers.
The hosts took an early lead through Chris Brunt, whose first-time shot flew into the roof of the net in the eighth minute after he was set up by Billy Jones.
Wolves had chances to level in an open game with Roger Johnson heading wide midway through the second half but West Brom secured the points when substitute Peter Odemwingie drove a low shot into the bottom corner on 75 minutes.
Victory propelled Roy Hodgson's side out of the relegation zone to 12th, while Wolves hover one point above the drop area in 16th.
Newcastle United will be looking to maintain their unbeaten start to the season at home to Tottenham Hotspur later in the day.
Manchester City overtook champions Manchester United at the top on Saturday with a 4-1 victory over Aston Villa after United could only draw 1-1 at Liverpool.
(Editing by Justin Palmer)
