The Blues won 3-1 to stay third, seven points behind leaders Manchester United but having played a game more.
Sunderland: Fernando Torres scored twice to make it four goals this week as Chelsea beat Sunderland 3-1 on Saturday to record their first victory in eight Premier League matches.
Torres, who also hit a double in the 6-1 thrashing of FC Nordsjaelland on Wednesday to end a month-long barren run in front of goal, volleyed the ball into the net with the studs of his boot in the 11th minute.
The Spain striker converted a penalty in the 45th, his first in English football, after Sunderland midfielder Seb Larsson's needless foul on Ramires as the ball was just about to go out for a goal kick.
Torres had seven goals in 21 matches in all competitions this season under Roberto Di Matteo. He has now scored four in five games under the Italian's successor and his former manager at Liverpool, Rafa Benitez.
Torres could have had a hat trick but his left-footed strike in the 48th hit the goal-frame, the rebound falling for Juan Mata to make it 3-0.
Sunderland had a glimmer of hope when winger Adam Johnson scored his first goal at the Stadium of Light, his swerving shot from a tight angle flying past goalkeeper Petr Cech in the 66th and nestling inside the side-netting.
Sunderland suddenly had the impetus and pushed Chelsea back, with Johnson's free kick from distance testing Cech. But the visitors repelled numerous attacks without too much effort to win their first league match in seven weeks - since the 4-2 victory at Tottenham on Oct. 20 - and the first under Benitez.
Sunderland have only won twice in 23 league games under Martin O'Neill during the past two seasons, placing the manager under further pressure following speculation last week that he had been considering his position.
Chelsea stayed third, seven points behind leader Manchester United but having played a game more. Sunderland dropped into the relegation zone, two points from safety.