Everton were threatening to be chief party poopers as the Gunners celebrated their 125th anniversary.
But with just 20 minutes left, Van Persie took centre stage to thump in a stunning volley to take Arsenal into the top four.
It was not vintage Arsenal and chances were at a premium in a low-key game.
But three more points keeps the Londoners' Premier League revival in full tilt.
Gervinho got his bearings wrong after 15 minutes when he allowed Theo Walcott's low centre to run away from him in front of goal and Tony Hibbert eventually made the block.
Aaron Ramsey floated an effort just over before Tim Howard got down well to beat away Gervinho's angled drive.
There was a scare for Arsenal when Walcott fell awkwardly on his knee at the start of the second half but the England man soon returned to the action.
On 56 minutes, Walcott skipped past Leighton Baines and into the right side of the area, where his fierce angled drive was beaten away by Howard.
Thomas Vermaelen then had to be alert to put a deep cross from the left behind as Tim Cahill looked to ghost in at the far post.
Everton finally entered the final third at the other end but Phil Neville's chip floated over.
Then out of nothing, Van Persie netted a stunning volley to give Arsenal the lead.
Alex Song chipped the ball across the Everton backline, where van Persie had drifted behind his marker to dispatch a sublime left-footed strike in off the far post.
Everton sub Conor McAleny flashed a drive just wide in stoppage time but there was to be no denying Arsenal.
Arsenal: Szczesny, Djourou, Mertesacker, Koscielny, Vermaelen (Miquel 82), Arteta, Song, Walcott (Frimpong 89), Ramsey, Gervinho (Rosicky 83), Van Persie. Subs not used: Almunia, Arshavin, Chamakh, Benayoun. Booked: Arteta, Ramsey. Goals: Van Persie 70.
Everton: Howard, Hibbert, Heitinga, Jagielka, Baines, Coleman, Neville (McAleny 76), Fellaini, Bilyaletdinov (Gueye 76),Cahill, Saha (Distin 64). Subs not used: Mucha, Stracqualursi, Barkley, Vellios. Booked: Coleman, Distin.