West Ham have had a nightmarish start to their season, winning only one of their first five games - and losing the other four.
Giroud also missed a decent chance when he was unable to make a good enough contact with an attempted scissor-kick after being found by Jorginho.
He is replaced in attack by Michail Antonio, who is more at home on the wing.
Jorginho and N'Golo Kante are going to retain their place in the starting line up while Ross Barkley will head back to the bench and Cesc Fabregas will return to his usual role in midfield.
As a result, both coaches opted for a change as Giroud made for Alvaro Morata, while West Ham threw on Lucas Perez for Antonio after 65 minutes.
Twice in the second half Hazard's nature overrode his new role in this team, as he tried to play in Morata with an overly ambitious back-heel and a first-time aerial flick rather than attempting to trouble Fabianski himself.
After the break West Ham continued to frustrate Chelsea, while Yarmolenko curled a shot narrowly over.
Chelsea will be desperate to secure another three points, with Liverpool trailing them only by goal difference.
Sarri still has question marks in all areas. I know that in the future, probably, I will have to face some difficulties.
"Maybe in two, three or four months it will be a problem".
It's not hard to imagine Sarri's high defensive line being torn to shreds, particularly if Rudiger's injury deprives the Blues of all recovery speed.
Aitoliko beach in Greece covered in spider web
Scientists say the arachnids are merely enjoying the handsome weather and availability of food, taking the opportunity to "party". Chatzaki explained that the spiders were not risky for humans and would "have their party and soon die off".