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The Reds had a big scare moments later, though, with Mohammed Kudus lifting the ball over Alisson but seeing his effort come back off the bar.
The visitors grew in confidence in the second half, creating plenty of chances.
Were it not from Alisson, who stayed tall to deny Jarrod Bowen after West Ham's captain beat the offside trap, it might have been all square going into the final quarter of the game.
The reverse fixture in December was one-way traffic, with Liverpool running out 5-0 winners.
Diaz struck the bar moments later as Liverpool looked to retake the lead, but it was Van Dijk who proved the hero.
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Kudus still West Ham's danger-man
Mohammed Kudus looked like he was going to provide their best chance of scoring.
Left-back has been an issue for Liverpool in recent weeks, with Andy Robertson making way for Kostas Tsimikas this time around, and Kudus threatened down his side.
The first big chance came shortly after Liverpool's opener.
A fine burst early in the second half might have led to something more with an extra bit of pace to keep the ball in play, as he caused problems for a defender in Wan-Bissaka who has kept top players quiet this term.
Moments after West Ham's equaliser, Diaz showed he had more to offer
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