Andy Gray's ninth goal of the season gave Burnley caretaker boss Steve Davis a crucial victory at Leicester.
Davis, in charge after Steve Cotterill left, saw his side profit from early dominance when Gray scored on the turn after 23 minutes.
Leicester had to wait until the second half to create a chance, with Patrick Kisnorbo's header going off target.
Gareth McAuley and Stephen Clemence had long-range efforts in the closing stages, but they were on target.
Leicester caretaker boss Frank Burrows:
"We played poorly and I would be telling lies if I said anything else.
"We've got to take the criticism when we play poorly just as we accept the praise and pats on the back when we play well.
"The fans are entitled to voice their disapproval because they pay their money. The only way we can answer this and win back the respect of the fans is to target and win our next game against Bristol City."
Burnley caretaker boss Steve Davis:
"It was an excellent result for the club and I'm sure Steve will be pleased.
"Andy's in good scoring form but when he's not scoring he works so hard. I thought he was excellent.
"This has to be top of my list for football memories. Burnley is my club and everyone knows what it means to me."
Leicester: Fulop, McAuley, N'Gotty (Hume 60), Kisnorbo, Stearman, Kenton (Wesolowski 55), Campbell, Clemence, Mattock, Cort (John 56), Fryatt.
Subs Not Used: Henderson, Chambers.
Burnley: Kiraly, Alexander, Carlisle, Jordan (Mahon 42), Harley, Elliott, Spicer (James O'Connor 70), McCann, Lafferty (Akinbiyi 76), Gray, Blake.
Subs Not Used: Jensen, Jones.
Booked: Spicer, Lafferty, Elliott, Mahon, Alexander.
Goals: Gray 23.
Ref: Clive Penton (Sussex).