Timo Werner ended his 14 game goal drought with a finish at the back post in the 39th minute to double the advantage.
Chelsea started quickly as they were expected to in west London, and it was Marcos Alonso who had the first chance inside three minutes. Mateo Kovacic slipped it across to the Spaniard, but he could only fire straight at Karl Darlow.
Four minutes later and Chelsea should've been ahead. Two chances in quick succession from Cesar Azpilicueta, deflected over, and a header from Tammy Abraham from close range sailed wide.
Werner was left fiery after having to go off after having blood on his face, and Giroud made the instant impact off the bench. In the 31st minute he put Chelsea ahead from close range. Werner played the ball across the box for Darlow to parry, and the Frenchman fired into the back of the net to make it 1-0.
Werner's confidence has been at an all-time low in recent weeks and months, but the effort can never be faulted. But in the 33rd minute he had a glorious chance to put Thomas Tuchel's two goals ahead. Kovacic played a one-two with Giroud who then fed the German through, but he could only put over the bar.