The shot-stopper was in fine form at The Emirates as he denied the Toffees on a number of occasions to keep them out and help Arsenal claim a 2-0 victory in front of their home fans.
Cech is being preferred as Arsenal’s first choice between the posts this season in the Premier League by new boss Emery and the goalkeeper repaid his manager’s faith with a brilliant display on Sunday.
Emery has been tasked with steering Arsenal back into the top four this season after the Gunners finished in sixth place and without a trophy last term.
And Emery was full of praise for Cech after the goalkeeper’s fine performance for the north London side this weekend.
Speaking at his post-match news conference, Emery said: “I’m very happy with the goalkeepers who are working with us, Emi, Leno and Petr.
“Petr has a big experience and a big quality. He’s started the season very well and we think he’s giving us the performance we want.
“Today he showed us that he’s very good and continuing to work hard with this spirit every day. For the other goalkeepers, it’s the same.
“They’re doing very well and are working very hard to make sure they’re ready to give the team their best performance, like Cech today.”
Arsenal now switch their focus to League Cup affairs and their home clash against Brentford in the third round on Wednesday night.
The north London side have not won the Premier League title since their famous unbeaten triumph under Arsene Wenger in the 2003-04 campaign.
They brought in Emery as their new manager after Wenger opted to stand down at the end of last season.
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