Brendan Rodgers' side can look forward to meeting Southampton in their first FA Cup semi-final since 1982 thanks to Iheanacho's predatory finishing at the King Power Stadium.
He put Leicester ahead in Rodgers' 100th game in charge before Mason Greenwood equalised late in the first half. Youri Tielemans restored Leicester's lead and Nigeria striker Iheanacho wrapped up only their second win over United in 23 years and their first since 2014.
Leicester, who have never won the FA Cup and last reached the final in 1969, will head to Wembley to face Southampton in April. "I'm obviously delighted. It was a great performance. Every aspect of the game was complete," Rodgers said. "We showed courage to play against one of Europe's greatest teams. I told the players they were three games from history. Now it's two."