Bolton took the lead but goals from Nathan Ecclestone, David Amoo and Steve Irwin saw the Reds take a comfortable 3-1 lead at the interval.
Bolton started the second half the better team and pulled a goal back from the penalty spot to make it 3-2. Dean Bouzanis then made an excellent instinctive stop to deny Bolton captain Daniel Ward after Andre Wisdom had cleared off the line moments earlier.
Right-back Irwin restored Liverpool's two goal lead and their confidence with his second of the night 12 minutes from the end. It was an excellent run and an even better finish to wrap the night up.
"We are pleased to reach the semi-finals but it was pretty nervy at times and we had to work hard for our victory," said under 18's coach Hugh McAuley.
"I thought we started the game brightly but they took the lead against the run of play with an excellent goal.
"We came right back into it and scored three very good goals before half-time and looked very comfortable.
"They got back into it at 3-2 and then controlled the game for a longer period than what we would have liked, but Dean made a great save to keep us in the game.
"Stevie then scored an excellent goal to give us the win but credit to Bolton who played well and worked hard."