Marcus Chan
Heading into the game, the Toffees were on a torrid run of form, leaving them in 19th place in the Premier League table.
Arsenal meanwhile, were hoping to extend their lead at the top of the table over Manchester City to eight points.
However, new Everton boss Dyche delivered a defensive masterclass as his side proved too stubborn for Mikel Arteta’s high-flying Gunners to break through.
James Tarkowski’s 60th-minute header from a Dwight McNeil corner ended up being the winner as Everton recorded a vital win.
As a result of the win, they have climbed out of the relegation zone.
After the match, Morgan tweeted: “Dismal Arsenal performance today - we've been bullied around by one of the worst teams in the Premier League. Inexplicable.”
Everton’s official Twitter account hit back with a gif of Dyche smiling as the Toffees celebrated a famous victory.
In his post-match interview, Dyche said: “It’s all about the players and they are the focal point for me. They have taken a lot on this week. The minimum requirement is maximum effort and we saw that today.
“They have been in a position where it has not been nice for anyone. I still believe we can improve with our play.”
Match winner Tarkowski said: “It’s taken me a while, I need to score more. What a great time to do it and a great day. It’s back to work on Monday and we crack on.
“We’ve lacked that little bit of grit at times and that’s what the fans want. We’ve seen what it’s all about today.”
Pep Guardiola’s City side can cut the gap to just two points if they manage to win against Tottenham Hotspur on Sunday afternoon.
Topics: Everton, Arsenal, Sean Dyche, Football