The result saw the East Midlanders increase their lead over seventh-placed Sheffield United to eight points with a game in hand.
Not only did Coventry reduce a two-goal deficit, they also had the satisfaction of earning their first ever point at the Walkers Stadium, having lost all five previous visits.
The high-flying Foxes took a fourth-minute lead through Wales international Andy king.
Lloyd Dyer's dangerous cross into the penalty area was half cleared by James McPake to the left midfielder, who had time to control the ball before beating Keiren Westwood with a well-placed shot from 12 yards.
Westwood then dived low to his left to keep out a Martyn Waghorn free-kick, before Coventry conjured up their first chance with Chris Weale managing to cling on to Carl Baker's hooked shot from 10 yards.
But the home side were soon back on the offensive with Westwood tipping away an angled shot from Dyer, who had been released for a run on goal by Waghorn.
Promotion chasers Leicester then doubled their lead with a controversial goal on 20 minutes.
Paul Gallagher crossed from the right and, after King had crashed a header against the bar, a goal was given when the referee's assistant signalled that the downward rebound off the woodwork had crossed the line.
After Matt Oakley had tested Westwood from 20 yards, Coventry pulled a goal back on 54 minutes when Stephen Wright crossed and McGivern's attempted clearance fell to McPake, who hammered home from eight yards.
Leicester were unfortunate not to restore their two-goal cushion on 69 minutes when a Jack Hobbs goalbound drive struck Richard Wood.
Richie Wellens had a half-chance on 72 minutes but his curling shot from 20 yards drifted wide of the far post.
Leicester survived a scare on 78 minutes when first Weale beat away a Clinton Morrison effort with Nobby Solano well placed to clear Woods' follow up shot off the line.
But there was no denying Coventry on 87 minutes when a Martin Cranie shot was deflected into the path of Morrison, who slipped the ball inside for Gary Deegan to guide it home from five yards.