A first-half goal from Willian and an own-goal by Martin Kelly gave Chelsea their first win in three games.
Two heavily deflected shots provided the blues with all three points as they close the gap on fourth-placed Tottenham to just two points.
Patrick Van Aanholt's late goal was unable to inspire the visitors to a draw as Chelsea hung on for the three points.
Both sides have struggled for form recently with Crystal Palace sitting in the relegation zone this game provided the perfect chance to get their seasons back on track.
With a midweek game away to Barcelona, Antonio Conte's men got two early goals which looked to all-but confirm the victory.
It was Chelsea's in-form man who put the Blues ahead after 25 minutes.
The Brazilian raced infield from the left-hand side and struck the ball goalbound from outside the box but it was a deflection off James Tomkins that put the ball beyond Wayne Hennessey.
Willian's 20-yard strike marked his fifth goal in his last five games across all competitions.
Despite all of Chelsea's dominance they never got beyond the Eagles' backline and a long ranged effort looked like their best chance of opening the scoring.
Kelly own goal
Davide Zappacosta's heavily deflected shot touched Martin Kelly last before tumbling into an empty net.
When it rains it pours in the case of Crystal Palace as their bad luck continues.
The Italian defender was found in acres of space inside the visitor's box and his shot firstly deflected off the Palace goalkeeper and then eventually off a helpless Kelly.
Only 30 minutes into the game and already maximum points seemed to have been earned by Chelsea with no way back visible for Palace.
Patrick Van Aanholt struck for the second time in a week to give Chelsea a nerve-racking finish.
The defender scored with minutes to go and will bring their earlier disallowed goal under scrutiny as it could have changed the complexity of the remaining season.
Despite their late effort, Palace were unable to grab another goal with just minutes left and for the third league game in a row lose by a one-goal margin.
Palace second best
After disappointing results for both sides last time out, they were both looking to get their seasons back on track.
Chelsea dominated the majority of the early possession but it was the visitors who came closest to opening the scoring.
Andros Townsend almost got his second goal of the week just 12 minutes into the game, the midfielders half-volley flew just over the bar.
From then on in, it was the home side who pressed for the opener and it did not take them long to go ahead.
Palace barely had a sniff and were pinned back in their own third by the hosts, with Chelsea doing to the Eagles what Manchester City did to them last Sunday.
It looked like Chelsea were going to get their third just before half-time but Tomkins' goal-line block denied Olivier Giroud.
Giroud seemed to have scored his first league goal for his new club but Tomkins' sensational last-gasp clearance denied the French international.
Just minutes into the second 45 and Palace struck the woodwork through Alexander Sørloth's left-footed effort.
Some sloppy defending by the hosts allowed Sorloth through on goal but he bluffed his one-on-one chance as he cannoned his shot against the post.
Tomkins once again denied Chelsea their third with a superb block in his own box.
On his 50th game for Palace, Tomkins dived to the Eagle's rescue as his block denied another certain third goal for the hosts.
For the third time in the game, a miraculous defensive block denied Chelsea their third goal of the game.
This time it was Aaron Wan-Bissaka who denied the hosts - Chelsea really should have been out of sight by the hour mark.
Next up to deny Chelsea their third goal was the post, Giroud had a simple chance on goal after Marcos Alonso pulled it back to the Frenchman but he failed to convert.
It was starting to become worrying for Chelsea as they continued to waste chances and kept Palace alive in the game.