The Reds had taken the lead at Anfield thanks to Emre Can’s deflected shot in the ninth minute, but Chelsea soon fought back through Gary Cahill in the 14th minute.
The Blues then took a 2-1 lead when Diego Costa fired home in the 67th minute.
With Liverpool pressing for an equaliser, Steven Gerrard’s shot appeared to hit the hand of Cahill in the penalty box.
And despite loud protests from the Kop, referee Anthony Taylor waved play-on.
Chelsea then held on for the three points to extend their lead at the top of the table to nine points.
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