Ex-Burnley man David Nugent opened the scoring in the 35th minute, placing a left-footed finish beyond Tom Heaton from just outside the area, making it four goals in his last four league meetings with his former club.
Chris Wood put the result beyond doubt 12 minutes from time, getting the better of Michael Duff before unleashing a stunning volley to leave Leicester six points clear with a game in hand and needing just seven more points to seal promotion.
The result extended their unbeaten run to 19 matches, while Burnley's first home league loss since March last year ended their 16-match undefeated streak.
Jose Riga's men remain out of the bottom three on goal difference alone after Barnsley trounced relegation rivals Yeovil Town 4-1 at Huish Park.
Chris O'Grady put the visitors ahead in the 53rd minute, and Liam Lawrence added a second 11 minutes later before Luke Ayling pulled one back for the home side with 20 minutes to go.
The comeback never materialised however, as further goals from O'Grady and Dale Jennings rounded off an excellent day for Danny Wilson's men.
Blackburn replied through Michael Keane eight minutes later but when Simeon Jackson converted another penalty two minutes from time, Millwall looked set for a priceless victory until Joshua King's stoppage-time equaliser earned a share of the spoils.
Birmingham City's poor season continued with a 4-2 home defeat at the hands of Bournemouth while Doncaster Rovers won 2-1 at Leeds United.
Brighton and Hove Albion's play-off hopes were dealt a blow as they went down 2-0 at home to Middlesbrough, although they were aided by promotion rivals Ipswich Town and Nottingham Forest holding each other to a 1-1 draw.
