Mohamed Salah (19) and Sadio Mane (45+2) scored open goals after ruthless attacking moves during a rampant first half at Anfield and the home side added a third eight minutes after half-time when Mane stroked home, controversially from an offside position.
Daniel Sturridge came off the bench to score with his first touch of the game (88) to complete a miserable afternoon for Pellegrini, who started five new signings but had goalkeeper Lukasz Fabianski to thank for ensuring the scoreline was not even more comprehensive.
Liverpool dominated both the chances and the possession as they overwhelmed West Ham in the first half and took a deserved lead through Salah on 19 minutes.
Man of the match: James Milner
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