Leicester cruised into the last 16 of the Carabao Cup courtesy of a routine 3-0 win against Newport County on Tuesday.
The Foxes have returned to form in recent weeks in the Premier League, and continued their resurgence as James Justin put them ahead just before half time.
Jamie Vardy then scored twice in the second half to round off a comfortable evening for Brendan Rodgers' side.
Burnley had to survive a brief scare as they fell behind to Crawley Town when Dom Telford found the net in the 22nd minute.