Danny Drinkwater chipped in a free-kick and captain Wes Morgan got the better of Marcos Rojo to plant a downward header past David de Gea and into the net.
The Foxes thought they should have been handed a penalty when Riyad Mahrez tumbled past Rojo, but referee Michael Oliver waved away the appeals.
Morgan could have sent Claudio Ranieri’s men in ahead at the break, but his header flew over the bar.
The Foxes continued to look threatening in the second-half, Danny Simpson almost found has Shinji Okazaki in the box before the ball was cut out.
On the counter Mahrez weaved past two challenges and fired in a shot from 20 yards, but De Gea was able to punch clear.