Van Persie then struck in the final 10 minutes with a free-kick of his own to seal a vital win for the Gunners that lifts them up to 10th.
Sunderland's fourth league defeat of the season keeps them out of the relegation zone on goal difference alone, but there was a long period in which they looked good value for a point.
For the first half an hour, the Gunners played perhaps their football of the season as they terrorised the hapless Black Cats. Led by captain Van Persie, who looked in fearsome form, Arsenal had free rein on their own patch.
The first 30 second appeared the set the tone. Tomas Rosicky put his weighted pass into the path of Gervinho, who surged forward before squaring a pass across the edge of the box for Van Persie. The Dutchman turned the ball on to his right foot and fired a clinical low finish past Simon Mignolet. It was Van Persie's sixth goal in 11 Arsenal appearances this season, and the quickest Premier League strike of the season so far, beating Anthony Pilkington's strike after 49 seconds for Norwich on Saturday.
Van Persie was simply unplayable for a Sunderland defence devoid of organisation or leadership. He almost doubled Arsenal's lead in sublime fashion when his chip came back off the far post after an exquisite turn past Kieran Richardson.
Sunderland were being run ragged, but they were given a flash of hope when Stephane Sessegnon - operating as a lone front man with no recognised striker in the visitor's starting line-up - beat the offside trap down the left. The Benin midfielder cut a pass back into the box, but Alex Song tracked back to intercept.
Still, that was enough to remind both sides that the gap was just a single goal, and Larsson wiped that deficit just minutes later with a dead-ball strike that was impressive even by the Swede's own high standards.
As Arsenal reacted to that equaliser by retreating within themselves, a buoyant Sunderland could have taken the lead. Larsson nudged Carl Jenkinson off the ball with ease and sent Sessegnon free to put in a cross, only for Wojciech Szczesny to block Lee Cattermole's close-range header. Young midfielder Jack Colback then spurned a chance to open his Sunderland account just before the break when he volleyed Larsson's cross over the bar.
The highly influential Rosicky send Van Persie free inside the area, and the striker's shot at the near post was blocked by Mignolet's boot with Gervinho waiting for the cross.
Andrei Arshavin came off the bench and almost scored a sublime goal when he slalomed through three Sunderland defenders only to fire a low shot just wide of the far post.
It was up to Van Persie to settle the affair for the Gunners with 83 minutes on the clock. The Dutchman placed the ball for a free-kick by the right-hand corner of the penalty area, and he curled his shot over the wall and inside the near post for his 23rd goal in 25 Premier League appearances in 2011.
Sunderland kept the Arsenal defenders honest in the closing stages, in particular substitute Ji Dong-Won who had the ball in the back of the net but was offside when he did so.
Arsenal's next fixture is Wednesday's Champions League trip to Marseille, while Sunderland face a visit to Bolton next Saturday in what already looks to be a key clash in the relegation battle.