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Chelsea got off to a positive and attacking start, coming close to taking the lead in the first 10 minutes.
But it wasn't long before the home team took the lead through Willian.
Seven minutes later, Chelsea doubled their lead when Davide Zappacosta's shot took three deflections near the goal line which was eventually awarded as a Martin Kelly own goal.
The introduction of Wilfried Zaha right after the interval provided some influence to Crystal Palace's attack.
A counterattack by the Blues early in the second half was about to be finished by Willian but his shot was blocked by James Tomkins.
Olivier Giroud had several chances of opening his account for the Blues but was unlucky to not be rewarded as his shot hit the post.
However, Palace scored through Patrick Van Aanholt to provide a late scare but wasn't enough as the Champions hung on for a 2-1 win.
The win moves Chelsea to 56 points as they ended their two-match losing run in the Premier League whereas Palace's losing streak is up to four games and they remain in the bottom three.
Here are the player ratings
Chelsea
Thibaut Courtois - 6/10
A left-footed Patrick van Aanholt shot was comfortably saved by the Belgian. Did not have much threat on his goal until the Palace fullback scored late to provide a scare.
Cesar Azpilicueta - 7/10
Once again, Azpilicueta was one of Chelsea's best defenders. Commanded leadership at the back completing a total of four tackles and six interceptions.
Andreas Christensen - 6/10
The Dane finished the game with a pass accuracy of 97%. Won two aerial battles and completed four long balls.
Gary Cahill - 7/10
It was a surprisingly good game for the Chelsea skipper as his side won the game with his inclusion in the starting lineup.
He, however, did a good job in defence, completing nine clearances.
Davide Zappacosta - 7/10
Provided good attacking threat with his runs and crosses.
The Italian played his part in the second goal as his shot wasn't cleared off successfully on the line by the Palace defence hence, it went down as an own goal as Martin Kelly got the last touch.
Zappacosta had a total of 14 crosses in the entire game.
N'Golo Kante - 7/10
The Frenchman had 81 touches and did not have much of a difficult game but did his job when called upon. Kante had a total of three tackles, two key passes and six long balls.
Cesc Fabregas - 6/10
The Spaniard did not have much of an influence but did complete a total of three key passes along with a whopping nine long balls and seven crosses.
Marcos Alonso - 5/10
Despite having two shots, Alonso did not have a significant contribution as he had only 69 touches and put in only one accurate cross in the box.
Willian - 8/10
The Brazilian scored the opening goal through a low shot from outside the post with the help of a slight deflection off the opposition defender.
He had another great chance following the counter-attack he started but was denied by Tomkins.
Olivier Giroud - 7/10
Giroud had a glorious chance of opening his account from 10 yards out but was denied on the goal line by Tomkins.
The Frenchman worked hard, getting into spaces and was unlucky to not find the net hitting the post. Came off in the 72nd minute to a standing ovation of the Chelsea fans.
Eden Hazard - 8/10
Hazard got past the Palace defence with his dribbling and played a short pass to Giroud but the Frenchman failed to convert it.
He was back to his best playing on his preferred left wing role, creating chances and getting in the box.
The Chelsea superstar finished the game with two shots, six key passes and eight dribbles.
Substitutes
Alvaro Morata - N/A
Replaced Giroud in the 72nd minute and did not have much of a contribution.
Tiemoue Bakayoko - N/A
Came on for Hazard late in the game.
Pedro - N/A
Replaced his countryman Cesc Fabregas in the 88th minute.
Crystal Palace
Wayne Hennessey - 6/10
Hennessey couldn't do much to save the second goal when the ball hit the back of his head before another deflection. Made a good save with his legs while facing Hazard one on one.
Martin Kelly - 4/10
Kelly put the ball in his own net after his failed first attempt at clearance came of his own teammate before deflecting back off him into the net.
James Tomkins - 6/10
Tomkins was the best defender for Palace as he made two blocks. First, he made an excellent goal-line block off Giroud's shot just before halftime.
He was it again to deny Willian following a Chelsea counter-attack.
Aaron Wan-Bissaka - 5/10
Miscued his cross in the last minute of the game squandering Palace's hopes of securing a point.
Going forward, he wasn't much of a threat as he had zero key passes and only one good cross.
Patrick van Aanholt - 6/10
The Dutchman put in a great left-footed strike from around the box but went straight into the hands of Courtois.
However, he did score his second goal in consecutive games late towards the end of the game to give his side the hope of securing a point.
Andros Townsend - 5/10
Townsend had three shots but none of them were on target. He did not provide any threat on the right flank as he failed to provide any good service into the box with his inaccurate crossing.
James McArthur - 5/10
McArthur had a decent game defensively as he accumulated two tackles and three clearances but did not provide any edge going forward.
Luka Milivojevic - 6/10
The Serbian was once again Crystal Palace's only consistent player. He had a pass success rate of 87% along with his two crosses and eight accurate long balls.
Jeffrey Schlupp - 5/10
Schlupp did not provide much threat on the left when his team got the ball. Had a pass accuracy of only 68% and had zero crosses in the game before being substituted off.
Christian Benteke - 4/10
The Belgian had a poor game as he failed to register a shot on target. His bad ball control resulted in Palace losing the ball on three different times and was substituted at halftime.
Alexander Sorloth - 5/10
Came close to scoring but his shot hit the post. Scored in the 85th minute but his goal was disallowed as a result of a foul by his teammate.
Substitutes
Wilfried Zaha - 7/10
Came on for Benteke straight after the halftime break. Zaha provided the much-needed spark for his team going forward especially with his runs and dribbles, giving his side the required lift offensively as he put in three key passes and got his teammates involved.
Jairo Riedewald - N/A
Replaced Jeffrey Schlupp in the 75th minute.
Lee Chung-Yong - N/A
Came in as a direct swap for Andros Townsend in the 81st minute.
