The Foxes, whose three away games have ended in defeat, were up against it when Dean Marney fired in an early opener to give Burnley the lead.
But David Nugent levelled matters with the second half only two minutes old, finishing from close range before Jamie Vardy scored his first home goal for the club with a neat finish to seal the points 10 minutes later.
Elsewhere, a comical own goal from Tommy Smith and a terrific strike from Mali international Tongo Doumbia handed Wolves a 2-0 victory at Ipswich - their first away win under new manager Stale Solbakken.
But it was far from funny for Ipswich boss Paul Jewell. The pressure mounted on his shoulders as his Tractor Boys remained second from bottom of the npower Championship with the worst goalscoring record in the division.
Smith's own goal arrived in the 66th minute when he inadvertently turned in Bakary Sako's free-kick from the edge of the six-yard box. And substitute Doumbia doubled the Molineux men's advantage after 77 minutes when he drilled a delightful right-footed shot beyond the helpless Scott Loach from 22 yards.
Huddersfield climbed into the top six with a 3-1 victory in an action-packed derby with Sheffield Wednesday which saw both sides reduced to 10 men.
It was a deserved third league win of the season for Simon Grayson's side, who took the lead through Oliver Norwood when he followed up his first-half penalty that goalkeeper Chris Kirkland had saved.
Lee Novak headed home Town's second two minutes later and although Wednesday defender Reda Johnson headed home before the break, Adam Clayton converted another controversial penalty in the 71st minute to condemn Dave Jones' men to a third straight defeat.
Source: PA
Source: PA