New acquisition Virgil van Dijk had the winning goal as Liverpool edged Everton 2-1 in the third round of the FA Cup here, while Romelu Lukaku returned from injury to score for Manchester United in 2-0 win over Derby County.
The Reds took a 1-0 lead in the first half when James Milner converted from the spot on Friday, reports Efe.
Everton were more aggressive in the second period, equalising in the 67th minute with a goal by Gylfi Sigurdsson.
With six minutes left in regulation at Anfield, Van Dijk headed-in Alex Oxlade-Chamberlain's corner to give Liverpool the victory.
To score the winning goal in the Merseyside derby was an auspicious debut for Van Dijk, who joined Liverpool from Southampton for £75 million ($100 million), a record transfer fee for a defender.
Just up the road at Old Trafford, United struggled more than expected against second-division Derby, who benefited from a solid performance by goalkeeper Scott Carson.
The English Premier League (EPL) side didn't open the scoring until the 83rd minute, when Jesse Lingard scored with a magnificent effort from distance.
Lukaku, who came on in the second half as a sub, sealed the triumph with a goal in the final minute of regulation.
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