West Ham had the ball in the Chelsea net twice in the first half, before and after Silva's goal.
Early in the game, Declan Rice's speed of thought and movement caught Chelsea out from a quick free-kick, and he finished expertly after getting around Mendy. But the assistant's flag was correctly raised after he was found to be slightly offside when the free-kick was taken.
Jarrod Bowen beat Mendy once as well, but that goal was disallowed for the young Englishman's foul on Silva.
In the second half, Chelsea had to withstand more pressure from West Ham, who were looking to barge the door open. Eventually, after they got through the spells of pressure, Chelsea scored twice in about 100 seconds, with both goals coming from Tammy Abraham.
Timo Werner's miscued shot fell on a plate for the big striker, who opened up his foot to place it past Fabianski. And then a couple of minutes later, Christian Pulisic headed a Mason Mount cross straight at Fabianski before Abraham thudded the rebound into an empty net.
Here's how each player fared for Frank Lampard's side.
Chelsea Player Ratings vs. West Ham United
Edouard Mendy - 6/10
Mendy didn't really have a save to make, but he was important in certain situations, as he came off his line to catch balls and take the pressure off the Chelsea defense.
Cesar Azpilicueta - 5/10
Azpilicueta was generally left isolated on the flank, as West Ham got overloads on him, with Cresswell overlapping, especially in the second half. He could not do much to stop crosses from the flank, but those in the middle managed to deal with it effectively.
Kurt Zouma - 7/10
Zouma was excellent, especially in the second half, in dealing with the barrage of West Ham crosses.
Thiago Silva - 8/10
Silva opened the scoring with a bullet header that Fabianski had no chance of stopping. He also was excellent, alongside Zouma, in dealing with crosses in the second half.
Ben Chilwell - N/A
On his birthday, Chilwell rolled his ankle in the opening exchanges while challenging Jarrod Bowen, which forced him to go off. He was replaced by Emerson Palmieri.
Jorginho - 5/10
Jorginho's return to Chelsea's Premier League squad didn't quite go to plan for the Italian. He gave the ball away in dangerous areas a couple of times. He was eventually replaced by Mateo Kovacic midway through the second half.
N'Golo Kante - 6/10
Kante had a couple of sloppy moments in the game, but those went unpunished. He played in a different position in this game, with Jorginho coming in at the base of midfield.
Mason Mount - 7/10
Mount was once again influential in being the link to glue together the Chelsea front three. He could've had an assist if Pulisic's header in the build-up to Abraham's second goal wasn't saved by Fabianski.
Christian Pulisic - 7/10
Pulisic was bright for most of the game but came alive to set up Chelsea's third goal. He first exchanged passes with Abraham in midfield, before putting the ball out wide. He didn't stand still as he got on the end of a Mount cross, which Fabianski saved excellently, only for Abraham to same home the rebound.
Timo Werner - 6/10
He did get himself an assist in this game, but that was off what was intended as a shot. He also missed three excellent chances to score and end his duck. but it wasn't to be. He even smashed the crossbar late in the game.
Tammy Abraham - 8/10
The two late goals turned Abraham's evening around, as it didn't start really well. In the end, he made the points secure for Chelsea with two routine finishes from close range.
Emerson Palmieri - 6/10
Emerson came on really early in the game, to replace the injured Chilwell. He largely did well in dealing with the big threat that Bowen posed from the right flank.
Mateo Kovacic - 6/10
Chelsea automatically looked a lot more secure when Kovacic slotted in on the right side of the midfield, with Kante going to the base of it.
Kai Havertz - N/A
Havertz replaced Pulisic for the final few minutes of the game.Published 22 Dec 2020, 05:23 IST