Clive Platt's header, his first goal for the Sky Blues, five minutes before the break looked destined to seal victory over a Foxes side who must have been wondering how they would be coming away from the game without the local bragging rights.
But King's sublime lofted finish in the 76th minute secured only a second point of the season for a visiting side whose passing football covered almost every blade of grass but lacked an end product.
The impressive Martyn Waghorn, making his second debut for Leicester after signing permanently from Sunderland, had handed the Sky Blues a firm warning had they needed one 11 minutes earlier when he headed against a post.
Coventry could count themselves lucky to still have their unbeaten home record intact although they have now won just one of their last 13 encounters against Leicester.
Aidy Boothroyd and opposite number Paulo Sousa made a combined total of 11 changes going into the derby clash.
And it was the visitors who were by far the better of the two sides from the off with Sky Blues centre-back Ben Turner doing well early on to block efforts from both the lively Lloyd Dyer and Waghorn.
The Foxes continued to orchestrate well-worked approach play as the half wore on but, crucially, Keiren Westwood - back between the posts after he and Boothroyd drew a line under their public contract dispute - was yet to be seriously tested.
Matty Fryatt rounded the Republic of Ireland international before firing another Leicester chance wide from an acute angle as Coventry struggled to see any of the ball.
Boothroyd was left with no choice but to match the visitors' system as Michael McIndoe replaced Gary McSheffrey, who appeared to be carrying an injury, after 36 minutes.
And the substitution paid dividends just four minutes later as Coventry took the lead against the run of play.
McIndoe, with one of his first touches, delivered a pinpoint cross for Platt who shrugged off the attentions of Jack Hobbs to head down into the bottom corner and hand City a fortuitous half-time advantage.
Sousa's side started the second half in the same way they started the first, firmly on the front foot.
Waghorn brought a good save from Westwood before Dyer also forced him into action.
Coventry's rearguard was now coming under serious pressure and Waghorn came closest to finding the net for Leicester when he headed Matt Oakley's cross against a post.
Westwood then did well to turn Dyer's drive for a corner before King finally levelled matters with his second goal of the season.
Jordan Clarke and Turner made a mess of their defensive duties and King lobbed the ball over the advancing Westwood with a superb finish that dipped under the crossbar.
Leicester made all the late running in search of a winner but it was not to be as Coventry escaped with a point.