Cesc Fabregas scored a well-placed drive in the 40th minute to put the visitors ahead.
Chelsea were without Eden Hazard for the match, but still managed to get yet another three points on the board.
But it was a nervy finish and a narrow win for Antonio Conte’s side, who were wasteful throughout.
And Chelsea fans are relieved to have escaped from the Stadium of Light with a win – and thanked Thibaut Courtois for his fantastic last-minute save.
Click through the gallery above to see some of the best reaction from Chelsea fans.