An abject display by Everton and a classy one from the Gunners combined to give Wenger’s side a first Premier League win in four attempts since they beat leaders Leicester City in the middle of February.
It brought a difficult week — in which Arsenal had gone out of the FA Cup to Watford and the Champions League to Barcelona — to a positive end, although the Londoners remain 11 points behind Leicester and seemingly with only the remotest chance of winning a first title since 2004.
Wenger’s own position has come under scrutiny with many of the supporters he has served so well for almost 20 years running out of patience as the chances of winning something have ebbed away.
But according to the long-serving manager, those calling for change have not helped the cause as Arsenal’s challenge has faded away.
Wenger said: “What hurts me is that at the important moment of the season, we played in a sceptical environment.
"And I think after the Tottenham game where we played a very good game, played with 10 men against 11, and came back to 2-2, I couldn’t understand why.
“At the moment when you need everyone behind the team — in such an important moment, we had to hit that storm. From the media, ok. From our fans? It is a bit more difficult to take.”
Wenger wants to get the supporters back on side with the “attitude” of the team, to create a united front for the remainder of the season.
It may be too late to rescue Arsenal’s title ambitions but the Frenchman has no plans to fall on his sword and will need their backing in the longer term.
He added: “I think the club has moved forward a lot. I just want to continue that, you know. And show the quality of the football I like. That’s all I can do. I can take criticism, I’m in a public job, so I personally can take the criticism and I can use that.”
By the end of 90 minutes at Goodison Park, much of Arsenal’s travelling support had turned their attention away from Wenger and towards majority shareholder Stan Kroenke as they called for the American businessman, who they see as favouring a healthy balance sheet as much as a trophy collection, to get out of their club.
Everton have a wealthy new backer of their own in Farhad Moshiri and remain in the hunt for a trophy via the FA Cup, having knocked out Chelsea a week earlier to reach the semi-finals.
But it looked here as though they were the ones with all the problems as they subsided to an eighth home league defeat of the season and were again booed off by their supporters.
Seamus Coleman hit a post after 60 seconds but it never got that good again for Roberto Martinez’s side, which could well have lost by a bigger margin and seen the worst defensive record suffer further damage.
Arsenal revelled in the freedom they were allowed as Everton missed the leadership and organisational skills of suspended midfielder Gareth Barry.
Danny Welbeck put the Gunners ahead after six minutes as he rounded Joel Robles to score his fourth goal of an injury-hit season after Alexis Sanchez and Mesut Ozil sliced open the Toffees’ back line.
Alex Iwobi then doubled the lead before the break with an equally assured finished, showing pace and poise to claim the first of what may be many Arsenal goals for the Nigerian international forward, 19, on his first Premier League start.
“It was a fearful performance that makes no sense. I thought we were as bad as we have been this season,” admitted a puzzled Martinez.
“I don’t think mentally we enjoy playing at home and today, that affected our performance. Until now it has affected our results, but today it has affected our performance.
"I know there’s been a lot of talk about the semi-final but every game is vitally important. Unless you can show you are a player to drive Everton forward, it will be difficult to see how you can stay in the side.”
Robles 5; Coleman 6, Jagielka 6, Funes Mori 5, Baines 5; McCarthy 5, Besic 5 (Stones ht); Lennon 6, Barkley 6 (Deulofeu 73), Cleverley 5; Lukaku 6.
Howard, Kone, Niasse, Osman, Galloway.
Ospina 6, Bellerin 7, Gabriel 7, Koscielny 8, Monreal 7; Coquelin 7, Elneny 7; Sanchez 8, Ozil 8 (Gibbs 75), Iwobi 8 (Chambers 86); Welbeck 8 (Giroud 75).
Macey, Mertesacker, Chambers, Campbell, Walcott