The tie was evenly balanced until Jones — an academy product who made his first team debut last year — settled the contest with a superb curling shot from the edge of the area.
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Jurgen Klopp rested virtually all of his regular first team players, instead fielding a starting lineup that featured three teenagers and new signing Takumi Minamino.
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But thanks to Jones’ strike and three sharp first-half saves from goalkeeper Adrian, Klopp’s risk paid off.
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“The ball came to me and I only had one thing in mind — to shoot. Luckily enough it led to the match-winner and a great goal,” said Jones.
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“It’s massive for me and the rest of the young boys. At times it’s frustrating thinking you might get a chance but then having to sit on the bench and watch.
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“We proved that we are learning every day and trying to push for a place in the team.”
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It was a second consecutive defeat under new manager Carlo Ancelotti for Everton, which had started the game at Anfield brightly.
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Dominic Calvert-Lewin, Mason Holgate and Richarlison all forced excellent saves from Adrian in the first period as the visitors probed Liverpool’s goal with a series of testing crosses.
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Reds captain James Milner was first off injured after six minutes as he denied Calvert-Lewin in the box. He was replaced by 19-year-old Algerian Yasser Larouchi, making it four teenagers — including 16-year-old Harvey Elliott — on the pitch for Liverpool.
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But despite Everton’s chances, the youthful home side showed composure and enjoyed plenty of possession and territory in the first period.
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After the break, Liverpool came out stronger and played with greater tempo. Everton, meanwhile, was lackluster.
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Ancelotti introduced former Juventus striker Moise Kean in a bid to break the deadlock, but it was to be Liverpool and Jones’ day, the teenager scoring his first ever goal in sublime style on 71 minutes.
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The result means Liverpool remains undefeated in domestic fixtures this season and is unbeaten at Anfield since September 2018.
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In Sunday’s earlier FA Cup games, Tottenham drew 1-1 with Championship side Middlesborough.
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Ashley Fletcher had given the home side, currently 16th in the second tier of English football, a second-half lead before Lucas Moura’s header ensured the tie went to a replay.
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The Premier League’s two other sides in action on Sunday were victorious, Chelsea beating Nottingham Forest 2-0 and Sheffield United defeating fifth-tier side Fylde 2-1.
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