The goalkeeper was in fine form in their opening 1-1 draw.
The goalkeeper is one of three new signings at Goodison Park this summer after he completed a move from Fulham.
It is the second time he has played under manager Ronald Koeman, having spent last season with the Dutchman at Southampton.
Tottenham's Dele Alli in action with Everton's Mason Holgate and Ross Barkley
He was expected to play a back up role at the club, but has actually starred as first choice, starting their opening game against Tottenham on Saturday.
He justified his place though, with two fine saves to deny Vincent Janssen and Erik Lamela and secure his side a hard earned point.
Holgate was clearly impressed too, saying having a great goalkeeper like the Dutchman behind him makes his job all the easier.
“When you’re behind a goalkeeper like Stek it makes it a little bit easier for you as well because,” he told the club’s official website.
“He is very experienced and he’s talking a lot behind you. He made two great saves at the end there to keep us in the game.”
Everton's Tim Howard
It now remains to be seen if Stekelenburg remains as Everton’s number one this seasons.
Blues fans had been keen to see a new number one arrive this summer after Tim Howard struggled last year and Joel Robles failed to prove he is good enough when given the chance to impress.
Other than Stekelenburg though, nobody else has arrived at it seems he will be given the chance to establish himself unless the Blues have a late move planned.
Everton manager Ronald Koeman before the match