The first-half saw both sides spurn chances with Sadio Mane's effort pinging off the outside of the post as Liverpool lacked their usual clinical edge.
However, the deadlock was finally broken after 70 minutes when Georginio Wijnaldum's low drilled shot squirmed through the arms of goalkeeper Dean Henderson.
Leon Clarke had a chance to rescue a deserved point for Chris Wilder's side at the death but saw his effort soar over the bar with the win taking Jurgen Klopp's Champions League winners eight points clear at the top of the table.
Here are our player ratings from the game:
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