The defeat leave Maurizio Sarri’s men drifting away slowly from qualifying for European competition.
The hosts were rewarded for their fast start to the second half as Richarlison scored his first goal in eight home games, stretching back to December.
Calvert-Lewin outjumped David Luiz when attacking a right-sided corner and tests Kepa down low, with the loose ball bouncing nicely for the Brazilian to head home from a few yards out.
Chelsea Kepa dived to the right direction but punched his effort back to Sigurdsson, who took the penalty earlier and he converts the rebound to make the scoreline 2-0.
What hope does this defeat leave the Blues as they face Cardiff City next while Everton will take on West Ham after the international break.