Chelsea suffered their first defeat of the Premier League season as they were beaten by Manchester United, while Liverpool striker Luis Suarez was again to the fore as Everton came thundering back to earn a draw in the Merseyside derby.
Meanwhile Tottenham and Newcastle scraped past Southampton and West Brom respectively.
Manchester United closed the gap to a single point at the top of the Premier League as they got the better of nine-man Chelsea, triumphing 3-2 in a dramatic encounter at Stamford Bridge.
After battling back from two goals down to level, Chelsea had Branislav Ivanovic and Fernando Torres sent off before Javier Hernandez netted the winner to seal all three points for the visitors.
United, who started the day four points behind the Blues, burst out of the blocks with an early goal; Van Persie's strike clattering off a post and rebounding off an unsuspecting David Luiz inside four minutes.
They were soon two goals to the good when Van Persie netted his seventh league goal of the season, the former Arsenal striker lashing home Antonio Valencia's low cross from the right.
Juan Mata inspired Chelsea's fightback as he curled home a free-kick from the edge of the area after Wayne Rooney clattered Eden Hazard before Ramires nodded in Oscar's cross to equalise.
But the momentum soon swung firmly back in United's favour as Chelsea had two players sent off inside five minutes; Ivanovic was given a straight red for bringing down Ashley Young as the last man and then Torres was handed a second yellow for diving after Jonny Evans' challenge.
United immediately looked to capitalise on their numerical advantage, and Hernandez scored his third goal in two matches as he poked home from close range after Van Persie's initial attempt was cleared off the line.
Everton displayed all the qualities which have kept them in the top four this season to battle back and draw 2-2 with Liverpool, who blew a two-goal lead the 219th Merseyside derby.
When Luis Suarez headed in his sixth goal in eight league matches in the 20th minute, after Leighton Baines had earlier turned the Uruguay international's cross-shot into his own net, the Reds appeared in control at Goodison Park.
However, in a pulsating first half Leon Osman pulled one back almost immediately before Steven Naismith equalised 10 minutes before half-time.
Papiss Cisse deflected home a fortunate injury-time winner for Newcastle as Alan Pardew's men recovered from Romelu Lukaku's equaliser for West Brom to grab three Premier League points with a 2-1 victory at St James' Park.
Substitute Sammy Ameobi struck a left-foot shot from the edge of the box which took a heavy deflection off the back of Cisse and was cruelly diverted past Baggies keeper Ben Foster to seal the home side's win.
Demba Ba had netted his seventh goal in nine starts to give the Magpies a 35th-minute lead, but the dangerous Lukaku looked to have snatched the visitors a point when he headed home a Zoltan Gera cross 10 minutes into the second half.
The remaining 55 minutes subsequently failed to match what had gone before, and although both sides could have won it after the break, the point was enough to keep Everton in fourth, six points ahead of their near-neighbours.
Gareth Bale returned to haunt his former employers as Tottenham held on to win 2-1 at Southampton.
Spurs had not even scored - never mind won - on their five previous trips to St Mary's but dominated the first half on the south coast.
Bale gave the north Londoners the lead just 15 minutes into the match against the club with whom he began his career, heading home on his return to action following the birth of his first child.
Spurs deservedly doubled their advantage as half-time approached through Clint Dempsey, who directed home into an empty net after Jose Fonte's clearance off the line fell straight into his path.
A vastly-improved Saints side re-emerged for the second period and they reduced the deficit in the 66th minute when Jay Rodriguez lashed home his first Premier League goal.
Southampton continued to press for a leveller as the clock wound down but could not find an elusive second goal, much to the frustration of under-pressure manager Nigel Adkins.