LIVERPOOL 2 EVERTON 1Virgil van Dijk made a dream start to his Anfield career, scoring the winning goal on his debut for Liverpool, as they beat city rivals Everton 2-1 in a pulsating FA Cup third round tie on Friday.The Dutchman, signed last week from Southampton for a reported fee of 75 million pounds ($101.7 million), rose inside the area to head home an Alex Oxlade-Chamberlain corner in front of the Kop end in the 84th minute of what had been an enthralling Merseyside derby.“What a night. It was thoroughly deserved, it felt amazing to be out there, the goal is very special for me and my family,” said Van Dijk.“Playing at Anfield for Liverpool is a dream for every player. To score a goal is even more special.”Liverpool looked to have been frustrated after Gylfi Sigurdsson brought Everton level in the 67th minute after a brilliant counter-attack from Sam Allardyce’s side.That looked to have produced a repeat of the Premier League clash between the pair in December when Everton grabbed a 1-1 draw despite their rivals having had many more chances.But Van Dijk, bought to shore up Liverpool’s weakest link, the centre of their defence, proved his value at the other end of the field with his strength and aerial power delivering the killer blow.After a frenetic start, Liverpool had taken the lead through a 35th minute penalty from James Milner after Everton defender Mason Holgate had pulled down Adam Lallana in the box.It was in many ways an old-school derby with plenty of strong challenges, a high-tempo and end-to-end rhythm but it was Juergen Klopp’s side who created the greater openings.Everton’s Wayne Rooney, who had been booked in just the seventh minute for a late lunge on Joe Gomez, was substituted in the 52nd minute, probably to save him from the risk of a red-card as he looked close to loosing his cool.Gomez headed wide at the back post when he had been left unmarked at a 54th minute corner and a minute later Lallana poked the ball wide after being sent clear through on goal.Everton keeper Jordan Pickford produced a fine parry to keep out an Andy Robertson blast at the near post.The Toffees looked to have made Klopp’s men pay for failing to make the most of those chances with Sigurdsson’s cool side foot finish.But the world’s most expensive defender had other ideas.MANCHESTER UNITED 2 DERBY COUNTY 0Late goals by in-form Jesse Lingard and fit-again striker Romelu Lukaku helped Manchester United to reach the FA Cup fourth round as they ground out a 2-0 home win over Championship (second-tier) side Derby County on Friday.The visitors looked likely to force a replay before Lingard struck with a first-time shot in the 84th minute for his fourth goal in as many games after a fine brace in a 2-2 Premier League draw with Burnley and another in a 2-0 win over Everton.Lukaku, who returned from a head injury and came on as a halftime substitute for Henrikh Mkhitaryan, broke away and powered his shot past goalkeeper Scott Carson at the death as Derby threw men forward in search of an equaliser.The outcome pleased United manager Jose Mourinho, who praised Lingard and Carson after he produced a barrage of superb saves.“It was a great shot by Jesse Lingard in the top corner, he’s in a moment of confidence where things go well for him,” Mourinho told the BBC.“He’s a good professional and a fantastic kid in the dressing room.“I was feeling that we were close to scoring and we never stopped trying. But when you get past 80 minutes and the goal hasn’t come, you fear the second match. But the team kept trying so I knew the goal could arrive.”United had missed a string of chances as Lingard hit the post with a fierce arrowed shot several minutes before he broke the deadlock and Marcus Rashford also found the woodwork with a glancing header in the opening half.Carson kept out an array of stinging long range efforts, including three from Paul Pogba as United struggled to find a way through a resolute and well-organised visiting defence.Pinned back for much of the contest, Derby launched several dangerous raids as defender Marcus Olsson and midfielder Tom Lawrence came close for the Rams, who finally cracked in the closing stages.Carson was left clutching thin air as Lingard unleashed a swivelling shot into the top left corner from 18 metres and with Derby throwing caution to the wind, Lukaku raced clear to score his 16th goal for United in all competitions.