Lloyd Dyer gamne City a 22nd minute lead but it was only held for 10 mins before Paul Hayes scored an equaliser. Hayes had twice previously gone close and he eventually got his goal.
Scunthorpe went looking for the win but King's goal stunned the home side and took leicester top.
City are at home now to Crewe on Tuesday and then face Dagenhgam and Redbridge in the FA Cup on Saturday.