But the Sky Blues had other ideas and reduced their arrears through James McPake's sweet volley after the break.
And as they threw everything forward in the final 10 minutes in a bid to draw level, they were rewarded in the 87th minute when Gary Deegan tapped in from close range.
The draw sees Leicester move into fourth place on the back of a run of one defeat in 12 and needing a major capitulation if they are to miss out on the play-offs.
Coventry's faint hopes of a top-six berth remain intact after the point, but they will realistically have to record a flawless run-in if they are to make it.
Having made the 25-mile journey north up the M69, Chris Coleman would have keen for his men to settle quickly in a red-hot atmosphere at the Walkers Stadium.
But the Sky Blues were unable to negate a menacing Leicester start and the hosts found themselves ahead inside the opening four minutes.
Some intricate play down the left found Lloyd Dyer in space and after McPake made a hash of clearing Dyer's cross, the ball fell kindly to King, who sidefooted a composed finish into the bottom corner.
Leicester then doubled their lead in the 19th minute.
The pace of Dyer was a constant threat and Westwood again had to be at his best to deny a low shot after a quick break.
But after the resulting corner had been cleared, Paul Gallagher dinked in an inviting cross, which King met with a thumping header which crashed in off the underside of the bar.
The linesman immediately flagged to signal the ball had crossed the line, but TV replays were inconclusive.
Coventry were simply unable to live with a rampant Leicester side in the opening half-hour and Martyn Waghorn could have made it three, but he rifled just over the bar.
Coleman's side were eventually able to stem the tide, though, and came back into the game in the latter stages of the first half, but they could not make inroads against a mean home defence.
However, they needed less than 10 minutes of the second period to reduce the arrears when Martin Cranie's cross was headed back across goal and McPake atoned for his earlier error by sweetly volleying home from 12 yards.
And after dominating possession for a period of time the Sky Blues finally fashioned two glorious chances to level.
First Clinton Morrison's low shot was saved by the feet of Chris Weale and when the rebound ended up with Wood, his shot was expertly cleared off the line by Nolberto Solano.
But they were not to be denied and they earned a point with three minutes remaining when Deegan tapped in from close range after Morrison's centre.