With exits from the FA Cup and Champions League, the Gunners came into the game knowing that anything other than a win will see them slip further away from their fading title ambitions.
First-half goals by Danny Welbeck and Alex Iwobi, capped a dominant, incisive display by the Gunners, who ran out comfortable victors over the Tofees.
Welbeck put the visitors ahead in the 7th minute after following a clever through ball from Alexis Sanchez, before rounding Joel Robles and slotting home.
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Iwobi, who started his first Premier League game for the Gunners, marked the start with his first league goal just before half-time.
The Nigerian international, was picked out by Hector Bellerin and finished comfortably, placing his shot under the advancing Robles.
Everton threatened through Romelu Lukaku and Phil Jagielka but were unable to find the back of the net, with Arsenal substitute Olivier Giroud missing a late chance to add a third.
Arsene Wenger’s side moved eight points behind first-place Leicester, who play Crystal Palace later Saturday, but still needs the leaders and second-place Tottenham to collapse in the final eight games to stand a chance of winning a first league title since 2004.