Chelsea created their first real opening after 21 minutes when Eden Hazard cut inside before seeing his low strike tipped wide by Simon Mignolet.
Liverpool then came close to opening the scoring shortly before the break when former Chelsea man Mohamed Salah turned his marker before firing just wide from the edge of the area.
The hosts did manage to find the breakthrough in the 65th minute when Alex Oxlade-Chamberlain poked the ball into the path of Salah, who slotted calmly past Thibaut Courtois.
But Willian had the final say in the 85th minute, with what appeared to be a cross from the Brazil international looping over Mignolet and into the back of the net.
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