Arsenal enjoyed a first win at bogey ground Goodison Park since 2017 as Leandro Trossard's second-half goal decided an otherwise turgid encounter.
Embattled near the foot at the table, Everton settled in for a long afternoon of defending and managed to frustrate Mikel Arteta's side for long periods.
Although they held a near monopoly on possession, the Gunners failed to create a great deal but ultimately the game was settled by its outstanding moment of quality.
A short corner routine involving several of Arsenal's attacking players ended in Bukayo Saka cutting back for Trossard to steer a superb finish in off the post.
It was a far from convincing display from the visitors but they won't care having been frequently humbled at Goodison in recent times. Before Sunday, Arsene Wenger had been the last Arsenal manager to win away to the Blue half of Merseyside.
"It was a long time without a win here," Arteta said. "We played a great game, we didn't give anything away. We dominated the game and created numerous chances. The score should probably have been bigger."
For Everton it was another miserable day during a bleak period for the club. Now mired in relegation trouble after a winless start to the season, this latest defeat came days after owner Farhad Moshiri had announced a deal to sell the club to American investors 777 partners.
But with many reports casting doubt over the viability of the takeover, coupled with the team's dire form, these are dark times for manager Sean Dyche and his struggling side.
"I thought we would have more points on the board by now but you can't give the ball away that many times," Dyche said. "That link on transition was missing and we weren't effective enough. We are conceding softish goals. Our growth is where we are. There is a reality. Last season nothing was solved. I've said there is massive work to be done."
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