The 18 year-old Polish goalkeeper won praise from coach Alan Stubbs afterwards.
He told evertonfc.com: "Matty's not had the easiest of times in recent weeks. We have conceded goals and we have asked him a few questions. But to be fair to him he has come up trumps. He made some really good blocks and some very good saves.
"He has atoned for a few things. I'm really happy for him and hopefully he can build on that. As a keeper you are judged on concentration and that is what we have asked him to work on. He kept us in the game."