The Clarets won the top-of-the-table clash at Turf Moor, extending their winning run to seven matches, while the Foxes also triumphed, sending them above Harry Redknapp's sideBurnley cemented their place at the top of the Championship with a 2-0 win over QPR in a meeting between two promotion hopefuls on Saturday.
Sean Dyche's men made it seven straight league victories to go three points clear with a confident display as Danny Ings gave the hosts the lead at Turf Moor after 65 minutes as he slotted home after combining with strike partner Sam Vokes.
And in-form Ings secured the points from the penalty spot two minutes from time, converting from 12 yards after he had been felled by Joey Barton, to hand QPR their first Championship defeat of the season.
Leicester City moved above QPR into second place after beating Bournemouth 2-1. Winger Jamie Vardy proved to be the hero for Leicester as he scored the winner 19 minutes into the second half after Marc Pugh had cancelled out David Nugent's opener.
A 92nd-minute own goal from Steve Davies earned Blackburn Rovers a 2-2 draw at Blackpool.
Tom Ince and Jordan Rhodes traded penalties for the two sides in the early stages, before Dan Gosling put Blackpool back in front. However, there was to be a final twist as Davies headed into his own net after former Blackpool striker DJ Campbell and Jack Robinson had both been sent off for their part in a late brawl.
Striker Jon Stead's first goal since rejoining Huddersfield Town gave them a 3-2 win over local rivals Leeds United in an enthralling encounter, while midfielder Edward Upson scored a double as Yeovil Town beat Nottingham Forest 3-1.
A Matty Fryatt goal salvaged a 1-1 draw and a share of the spoils for winless Sheffield Wednesday at Barnsley, who had taken the lead through Marcus Pedersen.
Midfielder Liam Trotter scored an injury-time penalty as Millwall drew 1-1 at Reading, Steve Lomas' men earning a point despite Sean Morrison's opener and Nadjim Abdou's dismissal.
Elsewhere, Derby County drew 1-1 with Birmingham City and Bolton Wanderers were held to the same score by Ipswich Town.