The Gunners have been in a rich vein of form of late and after four matches of coming from behind, finally managed to score first then hold out for a vital three points on the road as Tottenham were held at home by Stoke City.
Everton were unlucky not have an equaliser in the 31st minute when Tim Cahill found Royston Drenthe in the area with the Dutchman firing home past Wojciech Szczesny but the goal was disallowed with the linesman wrongly adjudging the scorer offside.
Earlier, Aaron Ramsey should have scored in the seventh minute when he got on the end of a clever van Persie header but scuffed his shot way over the crossbar from close range before Toffees keeper Tim Howard came up with a vital block to deny van Persie who had found space in the area three minutes later.
On the stroke of half-time, Tomas Rosicky tested Howard with a well-taken half-volley from a tight angle just outside the area prior to van Persie being desperately unlucky 12 minutes into the second half when Kieran Gibbs found him in the centre of the area with a clever header but the Gunners skipper saw his shot cannon into the upright with Howard rooted to his spot.
Everton had just one shot on target for the entire 90 minutes and with less than 40% of possession, it would have been cruel if they came up with a leveler as Arsene Wenger's men moved back into the top three with another fighting win.
TRIBAL ASKS: Wenger has instilled a new strength into his Arsenal team. Is this the type of fighting outfit that can perhaps challenge for silverware next season?
Goodison Park, Liverpool