Goals from Estevao, Joao Pedro and Enzo Fernandez handed Chelsea a convincing win against Crystal Palace at Selhurst Park.
Palace also had Adam Wharton sent off in the second half, and a late goal from Chris Richards was not enough as they remain eight games without a win.
Jean-Philippe Mateta started for the home side despite the uncertainty around his future, and it was he who had the first big chance of the match. The Frenchman nicked the ball off Benoit Badiashile and ran through, but could not convert with Robert Sanchez standing strong to deny him.
Furthermore, Chelsea began to apply some pressure on the Crystal Palace backline, with Moises Caicedo and Enzo Fernandez getting a kind break of the ball just inside the area, but neither could convert.
Ismaila Sarr may feel he should have done better with an effort from a throw-in - which was flicked into his path by Reece James - but the AFCON winner could not divert his close-range shot on target.
It was the away side who got a lucky break as Jaydee Canvot played a poor pass-back into the path of Estevao, who held off Tyrick Mitchell to run through and fire his shot past Dean Henderson to score.
It was the Brazilian's first Premier League goal since early October, and he nearly added another just minutes later in similar fashion. However, the angle was too tight for a finish that time.
Chelsea were awarded a penalty as Joao Pedro's goal-bound shot was blocked by the hand of Canvot. After a lengthy VAR review, the Blues were awarded a penalty and presented with a glorious opportunity to double their lead.
Enzo Fernandez finally stepped up to slot the ball into the bottom corner with Henderson rooted to the spot.
Things went from bad to worse for Oliver Glasner's side as Wharton was sent off for a second yellow card.
However, Palace did grab a late consolation after Chelsea failed to clear a corner, which was eventually headed in by Richards.
Liam Rosenior grabbed his fourth win as Chelsea boss, but it was arguably the Blues' best performance since the Englishman's appointment, and their first away win since November.
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As for Palace, their winless run goes on, and it is now eight without a win in the Premier League. There is unrest and speculation off the pitch, and it is certainly reflecting in their performances as they sit 15th in the Premier League table.
