Van Persie’s heroics fired Arsenal to an eighth win in their last nine games in all competitions, with Arsene Wenger’s sixth-placed side twice coming from behind after trailing to goals from Frank Lampard and John Terry.
Terry was included in the Chelsea line-up after a difficult week when he found himself at the centre of an FA investigation into allegations of racial abuse directed at QPR defender Anton Ferdinand last weekend.
But the afternoon belonged to Dutch forward van Persie, who struck twice in the final five minutes to clinch the points after Juan Mata had levelled the scores at 3-3.
Andre Santos and Theo Walcott also scored for the Gunners and the manner of their victory will strengthen Wenger’s view that his side have moved on from a difficult start, which included a traumatic 8-2 defeat at Manchester United.
For Chelsea, though, a troubled week got worse with a second successive league defeat.
Terry was always going to be the focus of attention coming into the game after another troubled week for the Chelsea captain saw him accused of racism.
Against such a background, Terry might have allowed himself to be distracted by the off-field saga but his goal on the stroke of half-time confirmed his attention was trained solely on the game.
The same could not be said for a number of other defenders on both sides, however, whose lapses in concentration contributed to a hugely entertaining game.
From the moment Ashley Cole eased his way past Arsenal’s makeshift right back Johan Djourou to set up a second-minute chance for Fernando Torres, it was clear this would be an open game.
Lampard gave the home side the lead with a 14th-minute header from Mata’s cross, immediately after van Persie and Gervinho had spurned glaring opportunities for the visitors.
But with chances appearing at either end, it was quickly apparent that that would not be the final goal of the game.
Daniel Sturridge wasted a good chance to double the home side’s lead in the 29th minute and once again the miss proved to be costly, with van Persie responding with the equaliser seven minutes later.
The goal came from a swift, incisive passing move between Aaron Ramsey and Gervinho that ended with van Persie slotting in his 10th goal of the season.
Chelsea then gained their reward for shading the first half when Lampard’s corner was turned home by Terry.
Wenger maintained during Arsenal’s difficult start to the season that his side lacked nothing in character and team spirit.
And they drew on those qualities to force their way back into the game at the start of the second half.