Thiago Silva took advantage of the sloppy marking game on the corner in the tenth minute and nodded in 1-0 to Chelsea.
The home team then never released the accelerator.
In the second half, the guests also joined the increased pace.
West Ham had several chances to equalize.
But instead of a draw, they lost the match in two minutes.
Tammy Abraham twisted Timo Werner's loose shot to make it 2-0 in the 78th minute.
A couple of minutes later, he put 3-0 from a narrow angle and closed the match.
But the victory may have been expensive.
National team defender Ben Chilwell linked out an ankle injury just before the 1-0 goal.
He will most likely miss the derby against Arsenal on the second day.
Right-back Reece James is already on the injury list.
Chelsea are now climbing to fifth place in the Premier League, six points behind league leaders Liverpool.