Liverpool beat West Ham United by a lone goal from Nunez who fired just over from Thiago Alcantara’s pass.
Nunez opened the scoring in the 22nd minute as Uruguay forward met Kostas Tsimikas’s cross with a header that arrowed inside the far post.
Almost netting again two minutes later, Nunez pounced on a West Ham mistake and forced a good stop from Lukasz Fabianski.
Nunez was inches away from doubling Liverpool’s lead with a fierce volley from 12 yards that smacked off the post.
After all their pressure, Liverpool nearly surrendered the lead on the stroke of half-time.
Joe Gomez’s needless barge into Bowen was deemed a penalty after referee Stuart Attwell checked the pitchside monitor.
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But when Bowen picked himself up to take the spot-kick, he saw his effort well saved by Alisson.
Henderson’s drive was tipped over by Fabianski early in the second half, with Nunez motoring past Thilo Kehrer to fire narrowly off-target moments later.
Despite that flourish, West Ham finished strongly and Said Benrahma almost snatched an equaliser when he shot straight at Alisson after Gomez misjudged a cross.
Tomas Soucek looked certain to equalise in the final minutes but a brilliant block from James Milner preserved the points for Liverpool.