Michael Kightly scored the only goal of the game in the 65th minute to seal Burnley's first win in six league matches, enough to send them above Leicester and QPR, who both dropped points.
Leicester, who had been top at the start of the day, lost 3-1 at Brighton and Hove Albion while QPR were held 0-0 by Blackburn Rovers at Loftus Road.
At the Amex Stadium, Ashley Barnes opened the scoring for the hosts in the ninth minute before Craig Conway doubled the advantage on 28 minutes.
Andy King pulled one back for Nigel Pearson's side but Barnes made sure of the result with a penalty 13 minutes from time as Leicester lost their second successive game.
Derby County climbed to fourth with a fifth straight win - 5-1 at home to nine-man Blackpool.
The visitors had taken an early lead through Isaiah Osbourne but three goals in 12 minutes after half-time turned the match around.
Chris Martin got the equaliser from the spot on 47 minutes before putting Derby in front six minutes later, and Craig Bryson added a third in the 57th minute.
Martin completed his hat-trick with another penalty 12 minutes later after Neal Bishop had been sent off, before Angel Martinez became Blackpool's fifth red card in two matches, Richard Keogh completing a miserable afternoon for the visitors by rounding off the scoring in the 90th minute.
Three points behind Derby in fifth are local rivals Nottingham Forest, who won 1-0 at Sheffield Wednesday thanks to Simon Cox's 48th-minute winner.
Completing the play-off picture are Reading, despite going down 2-1 at home to Bournemouth.
Goals from Lewis Grabban and Matt Ritchie shortly before half-time put the visitors in command, with Adam Le Fondre's 90th-minute strike proving nothing more than consolation.
At the wrong end of the table, Yeovil Town and Charlton Athletic finished 2-2 in a result which does little for either side's hopes of pulling away from the bottom three.
The visitors took a two-goal lead into the break thanks to goals from Cameron Stewart and Johnnie Jackson, but they were pegged back by a Michael Morrison own goal on 72 minutes and an Ishmael Miller penalty four minutes later, before Jackson was dismissed 12 minutes from time for serious foul play.
Elsewhere, Birmingham City and Watford snatched last-gasp draws against Middlesbrough and Leeds United respectively, while there were wins for Bolton Wanderers, Ipswich Town and Millwall - who overcame Wigan Athletic, watched by incoming manager Uwe Rosler.
