Liverpool and Chelsea played out a disappointing stalemate at Anfield in Saturday's early kickoff.
The two giants, who have been in constant pursuit of major prizes in recent seasons, are currently locked well outside the top four.
Chelsea had an early Kai Havertz strike ruled out for offside by VAR and there was also a lively debut as a second-half substitute for 89m new boy Mykhailo Mudryk.
Liverpool goalkeeper Alisson saved well from another new Chelsea signing, defender Benoit Badiashile.
Liverpool's own 45m recruit Cody Gakpo was quiet. He did force one save from Kepa.
Blues midfielder Mason Mount said, "You know this is going to be a tough place to come. Overall, we controlled a lot of it.. We could have taken our chances.
"It has been tough lately, we want to win games. I feel like it is getting better and we are working hard today. We'll definitely take this today. The final passes weren't there, if it was maybe we score a few first half, but as I said, this is a tough place to come. They press you and force mistakes, like the second half and I think we came through that."
