Chelsea secured a tenth consecutive league win to stretch their lead at the top of the table to six points.
Cesc Fabregas scored the crucial goal for the Blues just before half time to maintain their stunning form under boss Antonio Conte.
The loss leaves Sunderland rooted to the bottom of the table and four points from safety.
Liverpool moved into second place in the table after a comfortable win at the Riverside Stadium.
Two goals from Adam Lallana and a strike from Divock Origi ensured Jurgen Klopp’s side returned to form as they overtake Arsenal on goal difference.