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Arsenal recovered from a terrible start to hand Carlo Ancelotti's Everton their first Premier League defeat since New Year's Day.
Dominic Calvert-Lewin finished acrobatically after Arsenal failed to deal with a free-kick in the first minute.
Arsenal were level in the 27th minute when Eddie Nketiah finished expertly past Jordan Pickford from Bukayo Saka's cross and six minutes later they were ahead when Pierre-Emerick Aubameyang raced clear and finished coolly.
Everton equalised in first-half stoppage time when Richarlison got the faintest of touches to a header from Yerry Mina to poke past Bernd Leno but Arsenal retook the lead when Aubameyang scored his second moments after the re-start.
Arsenal survived a late scare to climb to ninth in the table, two points behind Wolves.
As it stands, fifth place could be enough to earn a Champions League spot because second-placed Manchester City have been banned from Europe's elite competition for two seasons, pending an appeal.
On Saturday, Chelsea strengthened their grip on a top-four place by beating London rivals Tottenham 2-1 on a day overshadowed by controversial VAR decisions.
Officials ruled that Spurs midfielder Giovani Lo Celso did not deserve to be sent off for a stamp on Cesar Azpilicueta that Chelsea boss Frank Lampard called a "leg breaker".
There were also incidents involving the technology in Bournemouth's defeat at Burnley and Manchester City's win at Leicester.
Elsewhere, there were wins for Crystal Palace and Southampton while high-flying Sheffield United drew 1-1 with Brighton.
Liverpool host struggling West Ham at Anfield on Monday.
