Gareth Taylor’s side, further depleted by the absence of cup tied Alanna Kennedy and Ruby Mace, mounted the perfect response to Sunday's WSL defeat to Arsenal to continue our defence of the famous old trophy.
The home side came back fighting with an excellent performance as Shaw got off the mark at the Academy Stadium with a second half hat-trick.
Our reward for that victory over Leicester sees us face Chelsea at home in the last four.
City dominated possession throughout the game's opening exchanges, with Lauren Hemp testing Leicester stopper Demi Lambourne early on at the Academy Stadium.
However, Leicester weren't there to simply make up the numbers, with Jess Sigworth’s powerful 16th minute strike flying just over the crossbar, as the Foxes looked to upset the odds.
Gareth Taylor's side continued to knock on the Foxes' door throughout the first half, Hemp and fellow forward Jess Park both going close, but it was to no avail, with the two teams going in goalless at the break.
But our pressure finally told just one minute after the break, as striker Shaw tapped home from close-range after being played in by Hemp.
With the deadlock broken, City went in for the kill, and a second goal soon followed when Vicky Losada drove forward from midfield and rifled a stunning long-range drive into the top corner from the edge of the box.
It was one of the Spaniard's final acts of the game, as she was replaced after taking a knock in the first half, but with that substitution came the welcome return of lifelong City fan Keira Walsh, making her first club appearance of the season after overcoming a calf injury.
Things got even better for City just six minutes after Losada's strike, with a second goal from Shaw ensuring a place in the semi-finals was within touching distance just after the hour.
The goals just kept on coming as captain Alex Greenwood stroked home from the penalty spot in the 70th minute to make it 4-0 after Hemp was brought down inside the area.
A very happy Bunny then secured her first City hat-trick with a superb third and final goal to make it five on the night, but there was still time for Angeldahl to get in on the act and complete the scoring in the 87th minute.
A super six goals from City, as we reached yet another FA Cup semi-final in style.
HOW WE LINED UP
Angeldahl started in midfield alongside Caroline Weir, while Park and Hemp provided width for Shaw up front.
CITY XI | Taieb, Beckie, Scott, Greenwood (C), Stanway, Losada (Walsh 60'), Angeldahl, Weir (Coombs 72'), Park, Hemp (White 72'), Shaw.
SUBS | Keating.
LEICESTER XI | Lambourne, Howard, Tierney, Plumptre (C), Purfield, O'Brien, Smith, Pike, De Graaf, Flint, Sigsworth (Graham 84’)
SUBS | Harris, Bailey-Gayle, Cain, Camwell, Robinson, Powell
Player of the Match: Khadija 'Bunny' Shaw
A first Manchester City hat-trick for the Jamaican international was the cherry on top of an imperious display from Gareth Taylor's side.
Consistently in the right place at the right time, Shaw lead the line impressively, backing up her three goals with excellent linkup play to help City on our way to victory.
The clash marked City's 100th game at the Academy Stadium, including the 2016 Continental Cup Final.
City return to FA Women's Super League action with the visit of West Ham United on Sunday 3 October in a 14:00 kick-off.
News about Man City v Leicester
Taylor: Home advantage a real boost
Gareth Taylor says drawing a home tie against Chelsea gives the team a real boost for FA Cup semi-finals. Watch more.
Taylor: Everyone played their part
Gareth Taylor said he could not be more proud of his players for the way they pulled together to book City’s place in the Women’s FA Cup semi-finals. Read more.
Bunny Shaw: Hat-trick a 'wonderful' feeling
Khadija 'Bunny' Shaw says she couldn't be happier to have netted her first City hat-trick to help Gareth Taylor's side to the Women's FA Cup semi-finals. Watch more.
Greenwood: It was an honour to captain City
Alex Greenwood says she is honoured to have worn the captain's armband for City. Watch more.
City 6-0 Leicester: Women's FA Cup highlights
Watch the best of the action from Manchester City’s 6-0 win over Leicester City in the Women’s FA Cup. Watch more.