The victory follows on from Sunderland's 2-2 draw against Manchester City in midweek, although they have persistently dropped points against the sides around them in the table this season.
"I think with us, Sunderland, this year anything can happen," Poyet is quoted as saying by Sky Sports News. "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.
"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 talking in the dressing room was that we'd rather play Real Madrid next Sunday and not Cardiff.
"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."
Sunderland face Manchester United, West Bromwich Albion and Swansea City following next weekend's clash against Cardiff City.