Arsenal kept their first clean sheet of the season and had 36-year-old Cech to thank for keeping the visitors at bay in the first half.
There were plenty of empty seats around the Emirates and, with Arsenal struggling to find any rhythm, those who had shown up were growing restless by the time Lucas Digne's free-kick was tipped over by Cech.
'I think this is what we lacked since I arrived in the last three years.
Theo Walcott scored 56 times at the Emirates during his 12 years with Arsenal and the Everton winger, making his second return to his old club, nearly added to that total just before half-time.
"Sometimes you need to make sure you win ugly games when you are not completely playing well and you just dig deep and you just closed the back door and win 1-0 no matter how".
In response to Cazorla saying that Arsenal lacked self belief to win the top trophies the experienced Cech said: "For any club who've won titles in recent years you have that knowhow how to finish it off".
Mourinho confirms two players to miss Wolves clash through injury
It is also about getting the right ones and I think they've got good young players and got also good experienced, stable players". However, a wonder-strike from Joao Moutinho before the hour mark levelled the match to earn the away side a deserved point.
"This club hasn't won the league for over 10 years so obviously you need to get back to knowing how to do it".
"We started with the new manager from scratch basically and we try to get this mentality of winning every game, progressing every game, working every day". In that moment we had just one player in our box, it is too clear for the assistant.
"Our team came to play and press high, but their goalkeeper is the best player on the pitch, and I think it reflects our performance".
They had a glorious chance to take the lead inside 90 seconds as Dominic Calvert-Lewin broke behind Arsenal's high defensive line.
The win over Everton moved Arsenal up to sixth in the table after a fourth consecutive league win.
Joining from Lyon in the summer of 2017, Lacazette enjoyed a good start to life at Arsenal scoring eight goals in his first 15 league games. It is an area where Arsenal have to improve if they want to become a title challenger this season.