Failure to win at Birmingham City next Saturday will mathematically confirm Sunderland's relegation from the Premiership after a record ninth successive defeat.
Sean Thornton gave the Black Cats hope of prolonging the inevitable with his first goal for the club in the 12th minute but an improved Chelsea performance in the second half led to goals from Gianfranco Zola and substitute Carlton Cole.
Thornton hit the post a minute after Cole's winner to leave Mick McCarthy still searching for his first point as Sunderland manager after three games in charge of a side short of confidence and goal scoring options.
Scotland international Kevin Kyle deputised for the injured Tore Andre Flo and his all-out aggression caused endless problems in the first half to a Chelsea side fortunate to be only one goal down at the interval.
Thornton chested down a weak headed clearance from Frank Lampard to beat goalkeeper Carlo Cudicini with a thumping drive from the edge of the penalty area and raise the spirits of the home fans desperate for a change in fortunes.
Only a brilliant save by Cudicini had prevented Kevin Phillips from opening the scoring in the third minute and Kyle missed a great chance five minutes after Thornton's strike when he failed to hit the target with a close range header.
Goalkeeper Thomas Sorensen twice thwarted Zola before Cudicini produced a stunning save to keep out Gavin McCann's fierce drive.
Zola though was not to be denied after Cole had headed on a William Gallas centre and a minute later a subdued Jimmy Floyd Hasselbaink had the ball in the net only to be pulled up for hand ball.
Cudicini kept out a thundering drive from Gavin McCann but after Hasselbaink headed over from close range, Cole scored a brilliant late winner.
"Cole's goal was amazing,'' enthused Chelsea manager Claudio Ranieri. "The boy has a lot of talent. That was a very important victory for us after losing in the Cup to Arsenal but Sunderland were better than us in the first half.'' McCarthy hailed his team's battling performance. "I thought it was a terrific performance and it has given me something to work on. We did not deserve to be beaten and it has taken a quality goal.
"We have worked hard against a quality team that is likely to finish in the Champions League next season and have set standards that I want at this club.''