Saturday night's win - which came after Poyet's players also drew 2-2 at title-chasing Manchester City in midweek - lifts the Black Cats to within three points of 17th-placed Norwich, with a better goal difference.
Few would have predicted the Wearsiders' last two results and Poyet is looking to keep up the momentum in the remaining four games of the campaign.
He told Sky Sports: "I think with us, Sunderland, this year anything can happen.
"It can go either way. When no-one expects anything from us, we get a result from Manchester City and now we beat Chelsea here.
"In a good way, I think, because there was not too much difference between the two teams, apart from the shots from distance.
"Today we got the breaks that for some reason have been going against us."
The win continued Sunderland's good record against the top teams, and Poyet admits they must now find a way to take points against those sides around them - with fellow strugglers Cardiff up next at the Stadium of Light a week on Sunday.
"The talking in the dressing room was that we'd rather play Real Madrid next Sunday and not Cardiff," he said.
"It's the way we play and feel more comfortable. We we feel we are, between brackets, the modest team we feel more secure.
"We can be calm. Sometimes when you play at home against teams around you you have to take the initiative. We are a little bit hurried and don't control the game."
Poyet suggested the penalty decision that decided the game after substitute Jozy Altidore was fouled by Cesar Azpilicueta in the box could have gone either way.
"It was very, very tough on the referee," he said.
"Every now and then you get it and every now and then you don't. It was the linesman who gave it straight away.
"We can talk about it for ages and even then we don't know for sure. We need to give the benefit of the doubt to the referee."