But the win came at a cost for the new Coventry boss. The game was held up for six minutes after a nasty looking injury to captain Stephen Hughes.
Marcus Hall made a fine block to deny Matt Oakley who let fly from 22 yards out but the home defender appeared to catch Hughes with his follow through and the midfielder crashed to the floor.
He was attended by a team of medics and the club doctor before being stretchered off and then taken to hospital by ambulance.
It took a while for both sides to pick up the pace of the game after the early incident. Kevin Thornton, who came on for Hughes, caused problems with his direct running from midfield and in the 14th minute won a free-kick in a dangerous area.
Danny Fox fired in from outside the area and when Ben Alnwick beat the ball out, it just evaded the on-rushing Leon Best.
At the other end, Andy Marshall did well to hold on to a bobbling shot from Iain Hume.
The game needed a goal and it came to the home side on the half hour mark, courtesy of referee Keith Stroud. Fox played a superb long pass to Best in the area. He and Gareth McAuley tussled, but there looked nothing untoward until the official blew up and pointed to the spot.
Coventry seemed as surprised as Leicester, but Elliott Ward gladly stroked the spot-kick home.
Thornton was a tad lucky to escape with just a yellow card when he appeared to catch Oakley late on the ankle.
Ian Holloway was forced to make chanegs either side of half-time because of injury and saw his side mount a spirited, if fruitless, comeback.
Despite establishing a territorial advantage they never really looked threatening enough inside the final third.
Their hopes were snuffed out 11 minutes from time when Best turned in a shot from a very tight angle after good work from Thornton.