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The Blues appeared to be employing sly time-wasting tactics from the outset, but Liverpool created an opening just after 10 minutes when Luis Suarez floated a diagonal ball to the back post, where Coutinho side-footed a volley into the side-netting.
The Reds went close again soon after when Suarez volleyed powerfully across the area, and Mamadou Sakho failed to control his shot and skied over the bar.
Suarez then flashed a shot over before Chelsea sneaked in front. Liverpool captain Steven Gerrard slipped in the middle of the park, allowing Demba Ba to race through on goal and slide the ball under Mignolet.
As things stand, Chelsea will close the gap on Liverpool to just two points with two games left.
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