The Toffees looked for the equaliser to take the match into a replay, but their Merseyside neighbours opted otherwise and progressed to the fourth round instead.
Liverpool manager Jurgen Klopp was understandably delighted after his calculated gamble of giving the majority of his first-team stars the day off paid dividends.
Liverpool boss Jurgen Klopp rang the changes as he named a young side to face Everton following a congested Christmas and New Year fixtures list, also handing new Japanese signing Takumi Minamino his debut after he joined from RB Salzburg.
"He's the best right now because he got a lot of stuff here", Adrian said.
"So, let me speak about Curtis - unbelievable player, Scouser, very confident".
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A substitution albeit forced three minutes later from the Reds signalled the end for veteran James Milner with Yasser Larouci replacing the utility player. And rightly so. He is in a very good way.
"Each individual was outstanding. sensational, I loved each second of the game". He's made big steps and will be a Liverpool player, if nothing unusual happens, 100 per cent. "I loved each second of it". I'm not surprised he scored that kind of goal.
"The defeat arrived because we were not able to keep a high intensity in the second (half)".
"He has still things to learn and improve, but you sometimes forget, and we forget it in training, that he is only 18". We went up from the back but we were too slow and had difficulty creating. "We lost energy and confidence".
Inevitable late pressure followed, but Liverpool held firm for a win that dealt a blow to Ancelotti in the early stages of his Everton tenure.