Richarlison had given the visitors a shock lead at the King Power as Everton produced a performance that may do enough to save manager Marco Silva's job ahead of the Merseyside derby on Wednesday.
But the introduction of Iheanacho just after the hour mark changed the game as the Nigerian set up Jamie Vardy to equalise and then dramatically scored the winner, which was initially ruled out for offside before a VAR review overturned the decision.
A sixth straight Premier League win sends Brendan Rodgers's men three points clear of defending champions Manchester City in second.
Silva was reportedly on the verge of losing his job earlier in the week after a run of just two wins in 10 league games that has left the Toffees hovering just above the relegation zone.