They were on the verge of more unwanted history after Marko Arnautovic gave West Ham a surprise lead at the Emirates Stadium.
It was the third successive defeat for the Hammers and their new manager Manuel Pellegrini, whose side made a promising start at the Emirates when Austria striker Arnautovic rifled in a fine low shot from 20 metres. 'We just need to be more efficient with our chances so that we score more goals.
Either way, the Spaniard finally got his maiden win to kick-start his tenure despite questions remaining over the defensive ability of his side.
"Every day, like I said, we talk, we laugh a lot, we work together when we are on the pitch", he said. We need to take them, anyway, if we're going to get any sort of result.
Accentuating the positives of Arsenal's spirited comeback, Emery added: "We improved in the second half and controlled more like we want".
"It was what I demanded of the players".
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Jolted into action by that shock setback, Arsenal were level within five minutes.
The Germany worldwide has now missed seven games in 20 months through illness and, with the player failing to justify his £300,000 a week wages, fans want answers.
Another former Arsenal player made an immediate impact as goalkeeper Lukasz Fabianski kept out Henrikh Mkhitaryan's strike with a tremendous stop.
The home side then fought back after Walcott and Michael Keane had put Everton two up, with goals in the last 15 minutes from Josh King, from the penalty spot, and Nathan Ake.
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Felipe Anderson continued to probe, flashing agonisingly across the face of goal in injury-time, meaning Arsenal nerves only settled when Welbeck swivelled to dispatch Bellerin's pass.