Everton had several chances to take the lead in the first-half but a combination of Adrian and poor finishing saw the Reds come out unscathed.
Jones looked the part in midfield alongside Pedro Chirivella and got his reward in the 71st minute as netted the winner with a spectacular curling effort from the edge of the box.
The youngster received the ball back after good work from Divock Origi as he unleashed a brilliant strike into the top right corner, giving Jordan Pickford no chance in goal.
It capped off a superb performance from Liverpool, whose youngsters showed fantastic grit and quality to emulate the usual first team’s style of play.
Liverpool will find out their fourth-round opponents in the draw on Monday night before travelling to London on Saturday for their Premier League meeting against Tottenham.
Slide through our gallery below for all the best photos from Anfield.