Leicester started brightly with striker Matt Fryatt twice going close but each time he was denied by a good save from Scunthorpe keeper Joe Murphy.
But it was a mistake by Murphy with a quickly-take free kick that opened the door for Leicester to take a 22nd-minute lead.
It was striker Lloyd Dyer who broke free into the box to punish Murphy for his mistake with a good finish.
That stirred Scunthorpe into action with striker Paul Hayes posing a threat to the visitors. First he turned well in the box to fire in a shot that was deflected just wide of the far post.
Then he did even better to wriggle his way into a shooting opportunity, only to be denied by a good save from keeper Paul Henderson.
Hayes though was not denied in the 32nd minute when he equalised with a fierce shot from an acute angle that found its way into the net off the foot of the far post.
Leicester too responded well and midfield man Bruno Berner went close to restoring their lead just before the interval with a shot that Murphy did well to save.
The second half was a much more cat-and-mouse affair with neither side wanting to make a mistake.
It was Scunthorpe who did most of the pressing but leading marksman Gary Hooper was marked out of the game by a well-drilled City defence in which Aleksandar Tunchev was a commanding figure.
It looked destined to remain a draw until the 81st minute when King ran through a square home defence to snatch the winner with a great finish from the edge of the box.