Frank Lampard's side have now gone 11 games unbeaten in all competitions and move up to third in the table ahead of Sunday's games. However, David McGoldrick's early strike did end a five-game run of clean sheets for the London side.
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Chelsea hit back 14 minutes later through Abraham who didn't hit the ball cleanly but got enough power on it to take it past Aaron Ramsdale in the opposition goal.
Drawing level gave Chelsea a boost and after several good chances Chilwell found the net with a right-footed shot from close range on 34 minutes.
However, the pressure continued to build and they couldn't keep Silva out after Hakim Ziyech sent a cross into the box and the defender headed the ball home.
After missing a great chance moments before, Werner made no mistake on 80 minutes with a powerful shot to make it 4-1 to Chelsea.
"We've come into this game on the back of a few clean sheets so it would've been nice to have another but the way we reacted after the first goal showed character," Chilwell said after the game. "Going 1-0 down against Sheffield United can be difficult, they're resilient and it was going to be a challenge but going down so soon and to win like that shows good character.
"It's a dream playing for Chelsea at the moment. Running forward having Reece James and Hakim Ziyech who want to come in and cross like that is perfect for me. I'm always being told to get on the back post so hopefully I can get a few more goals from there."