Striker Dirk Kuyt's 50th Liverpool goal gave his side a 1-0 victory in a fiery 213th Merseyside derby at Anfield which saw both teams reduced to 10 men.
The Dutchman scored for the fourth time in as many games with a close-range header 10 minutes after half-time.
Liverpool played the last 55 minutes at a numerical disadvantage after Sotirios Kyrgiakos was dismissed for a two-footed challenge on Marouane Fellaini, while Steven Pienaar was shown a second yellow in second-half injury time.
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