Sadio Mane gave the hosts an early lead when he played a one-two with Roberto Firmino and finished off an angled run with a shot into the far corner.
Jagielka flicked on a corner at the near post and, after Ashley Williams got a touch, Matthew Pennington arrived to slot in his first Everton goal on his first appearance of the season.
However, the lead lasted just two minutes and 57 seconds before Coutinho beat two players and curled a shot into the top corner, and he then set up substitute Divock Origi - on for the injured Mane - to power in Liverpool's third.
The result put the Reds seven points clear of fifth-placed Manchester United - who have three games in hand, including at home against West Brom later on today - while Everton are seven points off the top four having played more matches than their rivals.
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Labels: football highlights