Brendan Rodgers’ side will face Southampton at Wembley with Chelsea and Manchester City meeting in the other semi-final.
Leicester, who lost to eventual winners Tottenham in the 1982 semi-final, were the more vibrant and positive team against off-colour United as manager Ole Gunnar Solskjaer once again tasted defeat in the latter stages of a cup competition, his ploy of resting the likes of Bruno Fernandes and Luke Shaw failing to produce the desired result.
The Foxes’ hero was in-form striker Kelechi Iheanacho, who struck twice and now has nine goals in nine games.
He took advantage of Fred’s awful backpass to round Dean Henderson to score in the 24th minute after the hapless Brazilian was played into trouble by captain Harry Maguire.
Mason Greenwood crowned a crisp United move to equalise before half-time but Youri Tielemans restored Leicester City’s lead with a fine low shot seven minutes after the break before Iheanacho took advantage of shocking marking at a free-kick to head in Leicester’s third after 78 minutes.