The ex-Clarets boss insisted he did not have any “magic dust” to sprinkle on a struggling squad – the only one not to be strengthened by a January signing – but the effect he had was immediate as another former resident of Turf Moor James Tarkowski headed the winner on the hour.
It was the centre-back’s first goal since joining from Burnley on a free in the summer – and his first since the opening day of last season – and ended a run of no wins in 10 matches in all competitions.
The great escape is most definitely on for Everton, who by virtue of their lunchtime kick-off, briefly moved out of the relegation zone with hope springing eternal at Goodison after 12 miserable months under previous manager Frank Lampard.
Defeat was Arsenal’s first since September, and only their second in the league, and opened the door for Manchester City to close the five-point gap at Tottenham on Sunday.
The combination of Dyche – who has won two and drawn three of his last six meetings with the Gunners – and Goodison Park – where they have won twice in their last 11 visits – proved to be Arsenal’s nemesis once again as Everton won three successive home games against the Londoners for the first time in more than 45 years.
There was a protest march in the street ahead of kick-off – with the board of directors absent for the second match running on security advice – and a sit-in after the final whistle with a plane flying a ‘League’s worst run club #timetogobill’ (a reference to long-serving chairman Bill Kenwright) overhead early in the game.
But in between there was much greater optimism with Dyche making an immediate impact despite having just five days to work with his new squad.
Abdoulaye Doucoure – who had been training on his own after a fall-out with Lampard – made his first Premier League start since mid-August to bring some energy into a five-man midfield, which was a departure from the manager’s usual 4-4-2.
But what was evident on the pitch was reassuringly familiar with Dyche insisting his side be more direct and get the ball forward early to Dominic Calvert-Lewin, who looked re-energised having struggled for fitness all season, and he almost latched onto a Dwight McNeil pass but was out sprinted by goalkeeper Aaron Ramsdale.
Had Calvert-Lewis got more of a connection on Amadou Onana’s low cross after a bursting run down the left then Everton would have been ahead, with the England international also firing in a weak shot from Alex Iwobi’s knockdown and flicking a header wide after Iwobi and Seamus Coleman had combined on the opposite flank.
Doucoure was also making his presence felt and he too wasted a header from a McNeil cross as much-needed confidence flowed back into the side boosted by an encouraged and engaged Goodison Park.
Arsenal dominated possession but found it difficult to find a way through a more compact and committed opposition side, who were quick to get back into shape when they lost possession, with Conor Coady clearing the visitors’ best chance of the half off the line from Bukayo Saka’s volley.
And when Everton won four corners in two minutes Goodison roared its approval and, for a brief period, the Gunners were under pressure with the sight of Granit Xhaka hoofing a ball clear to no-one on the halfway line the most un-Arsenal of moments.
Being cheered off having out-shot and out-fought their opponents – eight was the most Arsenal had faced in the opening 45 minutes all season – was a new experience for players who had been booed at half-time of their previous two home games.
Martin Odegaard ballooned over from Eddie Nketiah’s cross early in the second half as Arsenal redoubled their efforts with new signings Leandro Trossard and Jorginho soon introduced.
But they had not had a touch before Tarkowski rose above a crowded six-yard box to head home a corner and get the old stadium rocking.
Neal Maupay replaced Calvert-Lewin as the Everton defensive rearguard began and his first intervention was to send Gabriel tumbling in the box, resulting in a VAR check for a penalty which came back to nothing.
It was the only negative response all afternoon for the hosts, who were cheered from first to last by supporters desperate for some relief from a second successive relegation battle.
Everton’s new-found resilience was highlighted by the fact goalkeeper Jordan Pickford did not make his first real save until the 78th minute when he batted away a Trossard shot to keep his first clean sheet in three months.