It took a 90th minute goal from Christian Pulisic to save Chelsea from dropping points again at Stamford Bridge.
Chelsea had experienced defeats at the Bridge in recent games and were looking to settle for a goalless draw before the American forward clinched a decisive goal to give them all three points.
Jorginho had the opportunity to hand the Blues victory through a penalty kick after Romelu Lukaku was fouled by Craig Dawson, but his lazy spot kick was caught by an alert Lukasz Fabianski.
The first half was a pretty much chance-less encounter with no firepower from both teams to make the game memorable.
Chelsea manager Thomas Tuchel had to leave out Reece James after the English defender felt something in his legs in training ahead of the West Ham game.
David Moyes chose his first eleven today with the Europa League Semi-finals in mind. Moyes placed his key men Declan Rice, Michail Antonio and Jarrod Bowen on the bench.