Neil Danns, who scored the winner against Derby at Pride Park nine days ago, saw a seventh-minute penalty brilliantly saved by Joe Murphy before David Nugent put the hosts ahead shortly afterwards.
Nugent then turned provider for his strike partner Jermaine Beckford to extend the lead after an hour.
Coventry could have got back into the game when they were awarded a 72nd-minute penalty but Sammy Clingan, like Danns, saw his spot-kick saved.
The hosts finished the game with 10 men after Paul Konchesky was shown a straight red card for a foul on Alex Nimely in the 83rd minute.
The three points saw Leicester climb a place to 11th in the table and narrow the gap on the teams in the top six to seven points.
A 10th straight away defeat means Coventry stay in the relegation zone and are three points adrift of safety.
Leicester manager Nigel Pearson named the same side that started the victory at Derby.
The only change to the Foxes squad saw Jeff Schlupp return from the knee injury he suffered at the start of the year. The teenage striker replaced Nathan Delfouneso, who has gone back to Aston Villa after his loan spell expired last week, on the bench.
Coventry's squad was unchanged but boss Andy Thorn made one alteration to his starting line up with David Bell replacing Carl Baker in midfield.
Bell almost immediately justified his inclusion with a first-minute goal but Kasper Schmeichel tipped his 12-yard effort wide.
Martin Cranie handed Leicester the chance to take the lead when he brought down Richie Wellens inside the area but Murphy got a strong hand to Danns' powerfully-taken penalty to divert the ball wide.
However, the Foxes were in front after 11 minutes.
Murphy parried a shot from Beckford but could only push the ball into the path of Nugent who blasted it home from six yards out, hurting himself in the process and requiring treatment.
Coventry responded well and Alex Nimely shaved the crossbar with a rising shot following a weaving run.
Leicester looked to have made sure of the points when Nugent played a neat one-two with Wellens before crossing for Beckford to tap home from virtually on the goalline.
However, Thorn's team rallied again and won a penalty of their own when Wes Morgan fouled Nimely. But Schmeichel matched Murphy's save earlier in the game to deny Clingan.
That took the wind out of Coventry's sails and the visitors even struggled to muster a chance following Konchesky's dismissal for what was deemed as a high challenge on Nimely.