Van Persie salutes the fans after his record-breaking goal
Theo Walcott scored a late equaliser as Arsenal saved themselves from a last-day defeat at Fulham.
The substitute finished off a driving run with a low finish that went in off the post to deny 10-man Fulham.
Steve Sidwell had opened the scoring when he sidefooted home following Bobby Zamora's cross before Robin van Persie slotted an equaliser.
Zamora's header made it 2-1 to Fulham, who then had Zoltan Gera sent off, before Walcott squared the match again.
The outcome meant both sides were unable to realise their final ambitions of the season - Arsenal had been hoping to snatch third place in the Premier League and with it the final automatic Champions League place, while Fulham were aiming to equal their best top-flight finish of seventh.
It was a match full of chances and entertainment played in an open style that took a little while to get going, but in the end was a decent finale to the season.
Hughes 'never feared for job'
Despite the potential prize of that automatic Champions League place on offer, there was a lack of urgency from Arsenal early on.
And even when they did fashion a chance for Samir Nasri, the midfielder headed goalwards so half-heartedly it might have raised further questions about commitment, following manager Arsene Wenger's pre-match demand for his side to show they deserve to wear the shirt.
Rustiness may have been to blame for Nasri's tame effort, seeing as he was returning from injury, but elsewhere there was also lack of care about Arsenal's play.
They did, however, create another good opportunity when Bacary Sagna sent a deep cross from the right to the back post and Kieran Gibbs headed downwards to force Mark Schwarzer into a decent stop.
Until that point Fulham had struggled to shake off an end-of-season lethargy but once Andrew Johnson had a sight at goal, testing keeper Wojciech Szczesny with a low effort, they gained some momentum.
Zamora began to cause problems, particularly down the right, and it was his break that led to Fulham's opener, the striker squaring the ball for Sidwell to slide his shot through the legs of both Johan Djourou and Szczesny.
Fulham threatened again when Zamora latched on to a through ball and lashed a shot wide from a difficult angle.
But it was Arsenal who scored next. Abou Diaby played the ball into the feet of Van Persie, who controlled the ball on the edge of the area and then sidefooted home with his next touch to score for the ninth consecutive away game in the Premier League.
It meant the Dutchman also equalled the record of 18 goals scored in a season from 1 January onwards held by Thierry Henry and Cristiano Ronaldo.
Wenger hints at summer of change
Fulham responded well and would have gone into the break in the lead but for some sharp defending from Thomas Vermaelen, who got back to stop Danny Murphy's goalbound poke.
The first chance of the the second half went Arsenal's way and it took a superb save by Schwarzer, clawing away Nasri's curling free-kick, to stop the visitors taking the lead.
After surviving that scare, Fulham redoubled their efforts and they were rewarded when an exquisite left-wing cross from Jonathan Greening was headed in by the lively Zamora - a just reward for the striker's impressive performance.
Zamora's attacking partner Johnson was also proving a problem for Arsenal's backline and the forward went close twice in quick succession.
In between those chances Arsenal were almost gifted an equaliser when Schwarzer fumbled Van Persie's cross and the rebound fell to Marouane Chamakh, but he could not direct his effort on target.
When Fulham's next opportunity came, Zamora was on hand to demonstrate a clinical touch, thumping home a header from Greening's cross.
The hosts seemed as though they would press home their advantage, with Simon Davies coming close with a toe-poked effort from the edge of the box.
But the tide changed when Gera was shown a straight red card for a two-footed lunge on Vermaelen.
Fulham went into this match in contention to earn a place in the Europa League through the Fair Play League. It remains to be seen whether Gera - such a central figure in the Cottagers' run to the 2010 final - will have cost them their involvement in next season's competition with his indiscretion.
Only once the final Fair Play table is published will it be clear who has qualified.
Arsenal - who had brought on Walcott, Andrey Arshavin and Emmanuel Eboue - sensed a chance to salvage something from the game.
And in the last minute of normal time, Walcott drove in from the right wing and shot low into the corner.
Arsenal boss Arsene Wenger
"It was an average game and in the end we felt the disappointment with fourth place because three weeks ago we were in the position to win the league.
"Of course we didn't lose our top-three place today, we lost it last week [with the 2-1 home defeat by Aston Villa] and that is why in the end we have to go through a qualifier."
He added: "We are frustrated, disappointed, but as well we have not to go overboard and think that our team is not good.
"We have to rectify some things in our squad and we will try to do it but it's not easy, even with money.
"Even if people say you have to spend money, we have to be realistic. We can't buy players for £50m. That is a fact. The amount of money is not always linked with the quality of player.
"First you have to find the right players and then turn up with the money - but if we find the right players we will spend the money."
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