Spurs have not won a league fixture against Arsenal since 1999, and they fell behind after Van Persie opened the scoring at the Emirates Stadium and Cesc Fabregas added the second after winning possession straight from the kick-off.
Both sides went into the weekend level on points, although Spurs had played a match extra. However, recent discussion that the gap between the clubs was closing was ended when Van Persie scored Arsenal's third after the break.
Spurs manager Harry Redknapp formation worked well initially. Arsenal fans were starting to get restless in frustration until the two goals in as many minutes just before the interval.
Gifted Possession
Spurs did not create much themselves but mostly limited their rivals to half-chances.
The match totally turned just before the break though. Cameroon full-back Benoit Assou-Ekotto's mistake gave possession to Fabregas on the edge of the area. The Arsenal skipper passed to Van Persie, who had keeper Gomes to beat but he hit his finish wide.
Arsenal's Arshavin then cut in from the right and had an effort deflected over by Vedran Corluka. However, the hosts were not made to wait long for their opening goal.
Bacary Sagna's low cross from the right was met by Van Persie and crept in at Gomes' near post.
Bursting Through
The second came 11 seconds after Spurs kicked off. Wilson Palacios tripped and Fabregas went on a fantastic run. He burst through challenges from the Honduras international and Tom Huddlestone. The Arsenal skipper then skipped around Ledley King and planted his finish past Gomes.
In the second half Arsenal looked to extend their lead. Eduardo, who replaced Nicklas Bendtner after he looked to have picked up an injury, was sent through by Fabregas and Gomes stood up well to save.
More pressure from Arsenal led to the third goal.
Eduardo had been floored by Assou-Ekotto. The assistant referee flagged for a foul but the ref allowed Sagna to continue after most had stopped.
Sagna's cross went through the barrier formed by Gomes and King, with Van Persie tapping in.
All Spurs had to show for their efforts was a David Bentley free-kick which was saved.
Eduardo should have added another when he broke the offside trap but his finish went just wide.
Match Quotes
"We took advantage of the shock of the first goal and in the second half we always played a little restricted. We were structured and did not give chances away. After the third there wasn't the impression that Spurs would come back." - Arsene Wenger
"The two quick goals we gave away turned the whole game upside down. I thought they were edgy, they were giving the ball away, the crowd was moaning at every mistake. I thought we were going to come in at half-time in great shape." - Harry Redknapp
