كتب : Omar AbdelAziz
The Spanish ace scored two quick second-half goals in the 59th and 63rd minutes to maintain the Reds' unbeaten run so far this season.
Liverpool jump to top temporarily with 14 points from six games, two ahead of Arsenal who host Hull City on Saturday.
Everton continue their poor start to the season, as they lie ninth with seven points.
The Toffees are yet to secure a point at home after six Premiership games, which included defeats to Blackburn Rovers and Portsmouth.