Substitute Kai Havertz scored the winner after Ben Chilwell, still working his way back from the knee injury he suffered last season, cancelled out a Michail Antonio opener for West Ham.
It was a frenetic end to the game after Maxwel Cornet appeared to have equalised following a mistake from Chelsea goalkeeper Edouard Mendy.
But VAR intervened and after a lengthy look called off the goal- and Chelsea held on to take all three points from the game.
The decision to cancel the West Ham goal has once again raised doubts over the real impact VAR is having on the game, but Thomas Tuchel says it was the right call as his goalkeeper was clearly fouled by Bowen.
He told reporters after the game at Stamford Bridge: “It was a clear foul on the goalkeeper and I even had doubts on the first goal as it was an irregular goal.
“It was not easy to keep the belief, it is hard to attack fluidly and create chances against West Ham, nobody plays an open, spectacular match against them.
“We take it now step by step, we will try to use this momentum - things are clear now, we can demand full commitment to everything. We are in the middle of creating this and it is not finished.”
The win over West ham is the perfect response to their defeat to Southampton in midweek and they will now travel to Croatia to take on Dinamo Zagreb in midweek with momentum and confidence from a hard fought victory.
There is also still new striker Pierre-Emerick Aubameyang to come into the team after he sealed a transfer deadline day move from Barcelona.
The Blues are now fifth on the league table in the Premier League and have another London derby against Fulham over the weekend.