Three minutes later Burnley were two goals ahead as Johann Berg Gudmundsson floated a cross deep to the back post, where Kevin Long was on hand to plant a firm header beyond Schmeichel and into the Foxes' net.
A shellshocked Leicester sprung into life and enjoyed several opportunities to reduce the deficit, with Riyad Mahrez and Jamie Vardy both missing good chances, but the Clarets retained their two-goal lead come the break.
Burnley came out brightly in the second half as Gudmundsson collected Wood's layoff and unleashed a left-footed effort from the edge of the area that sailed over the bar.
Leicester did succeed in halving the deficit on 72 minutes as Vardy picked up Kelechi Iheanacho's pass into the inside left channel and bore down on goal before slamming the ball beyond the reach of Pope.
However, Claude Puel's charges could not complete their comeback, ensuring that Burnley picked up three crucial points to remain hot on the heels of sixth-placed Arsenal, who are just two points ahead, while the Foxes remain eighth.
BURNLEY (4-4-2): Pope; Lowton, Long, Tarkowski, Ward; Gudmundsson, Westwood, Cork, Lennon; Barnes (Vokes 85'), Wood (Hendrick 75')
LEICESTER CITY (4-2-3-1): Schmeichel (Hamer 86'); Simpson, Morgan, Maguire, Chilwell; Silva, Choudhury; Mahrez, Okazaki (Iheanacho 46'), Gray (Diabate 64'); Vardy