Kelechi Iheanacho found the opener for the Foxes 25 minutes in after he capitalised on a poor pass-back from Fred rounding goalkeeper Dean Henderson and finishing to give the hosts the lead.
Mason Greenwood equalised for Ole Gunnar Solskjaer's men shortly before half-time with a composed finish from inside the box however Youri Tielemans put the Foxes back in-front shortly after the restart.
Iheanacho then got his second of the game after he headed home unmarked at the back post to secure Leicester's place in the last four and a trip to Wembley Stadium where they will face Southampton for a place in the Final.
Story of the Match
Vardy efforts spark life into the game
Up until the 15-minute mark the start to the game had been a cagey affair, with very little being created from either side, however it was the home side who had the first real chances of the game.
Some sloppy play from Fred saw the Brazilian surrender possession and allow Leicester to break forward and after the initial shot was stifled, Jamie Vardy was able to hit a low curling effort which was well saved by the feet of Henderson.
Moments later and the Foxes number nine looked to strike on goal again, but his shot was blocked by former teammate Harry Maguire.
Iheanacho takes advantage of Fred error
Fred had been treading on thin ice with his previous errors and in his case, it was third time unlucky as Iheanacho pounced on the midfielder's wayward pass.
Playing out from the back, captain Maguire's ball into the Brazilian midfielder saw him attempt to play the ball back to the centre-back, however his pass fell to the path of the in-form Nigerian.
Taking his time to compose himself and round the keeper, Iheanacho stroked home into an empty net to give the Foxes the lead.
Away side draw level
Leicester had controlled the play for large parts of the half, however on a rare first-half Manchester United attack, the Red Devils would draw level in the 38th minute through Mason Greenwood.
Alex Telles was able to break down the line on the left-hand side, driving a low ball into the box which evaded the Foxes backline but not the feet of the teenager, who adjusted himself well to fire the ball past Kasper Schmeichel and equalise.
The goal was Greenwood's first since United's Fourth Round win over rivals Liverpool and fifth of the season.
Tielemans fires foxes back in front
Like the first-half, it was the hosts controlling possession and their patience paid off as they restored their lead through Tielemans.
With all the time and space in the world, the Belgian was able to drive through the middle of the pitch following a neat one-two with Iheanacho as Vardy's run created space for the 23-year-old, dragging defenders out of position.
Tielemans reached the edge of the box and unleashed a stunning effort into the bottom corner, giving Henderson no chance of getting his fingertips to it.
Vardy squanders great opportunity
Leicester had a chance to extend their lead through Vardy on the verge of the hour but the striker was unable to capitalise.
Good work from Wilfred Ndidi to win the ball back enabled Iheanacho to thread through his strike partner who ran through on goal.
Beating Maguire with ease, the former England international had the goal at his mercy, however he dragged his shot the wrong side of the post - a chance you would've expected an in-form Vardy to have buried.
Iheanacho seals Wembley trip
Manchester United had failed to trouble the Leicester backline and were made to pay for their lacklustre display as Leicester found their third of the game.
Substitute Dennis Praet took the ball into the corner and was able to win the free-kick after a foul from Scott McTominay.
Marc Albrighton then delivered the ball into the box, finding Iheanacho free at the back post to head towards the goal, with Henderson only able to direct it into the roof of the net.
A great opportunity to win the cup
The night will be remembered for Leicester's exceptional performance but there will now be genuine belief in the Foxes camp that they can go on to win their first ever FA Cup.
Their reward for beating Manchester United is a tie against Southampton where Brendan Rodgers' side will be favourites to reach the final for the first time since 1969 where they will face the winner of either Chelsea or Manchester City.
100 games at the helm for Rodgers
Sunday's game marked 100 games in charge for Brendan Rodgers and he will have been delighted with his side's performance.
The East Midlanders were worthy winners and under the guidance of Rodgers, the club has been transformed of a side with aspirations of competing for trophies into a side that are now well in contention to win silverware.
Lacklustre United disappoint in the East Midlands
After their display in Milan on Thursday night, Ole Gunnar Solskjaer's side were polar opposite as they failed to seriously test Leicester's resolve.
Aside from Greenwood's equaliser and a Bruno Fernandes free-kick, the Red Devils were sluggish in play and looked like a side struggling for creative ideas.
Combined with a poor defensive decisions, United will look back on the tie with huge disappointment as the wait for a first trophy under Solskjaer goes on.