Sean Dyche's side lost their seven-match winning streak in the league at Millwall but would have been delighted just to come away with a point.
An upset looked to be on the cards after Scott McDonald and Danny Shittu had given the hosts an unlikely two-goal lead.
But Burnley striker Sam Vokes pulled a goal back in the 39th minute before an own goal from Australian Shane Lowry in the second half handed the table-toppers a point.
Leicester remained second after a convincing win at Vicarage Road in the early kick-off.
Returning to the scene of their play-off semi-final disappointment last season, Chris Wood, Anthony Knockaert and Lloyd Dyer scored for Nigel Pearson's side to set up a superb victory.
Meanwhile, QPR snapped a three-match winless streak with a 2-1 home win over Derby County.
Jermaine Jenas had given Harry Redknapp's side the lead after 11 minutes, only for Tottenham loanee Simon Dawkins to level proceedings.
But veteran defender Clint Hill scored the winner with 27 minutes to play as QPR returned to winning ways.
Blackpool created some breathing space in fourth place with a 1-0 win at Nottingham Forest, which came thanks to Stephen Dobbie's injury-time winner, while struggling Sheffield Wednesday caused the upset of the day with a 5-2 hammering of fifth-placed Reading.
Wednesday – who entered the game without a victory all season – turned on the style as a double from Matt Fryatt sank Nigel Adkins' side.
Miguel Antonio and Sunderland loanee Connor Wickham also scored for Wednesday, who benefited from a Sean Morrison own goal during the first half, as Pavel Pogrebnyak and Adam Le Fondre's efforts for the losers meant little.
Wednesday's win meant Yeovil Town dropped to the bottom of the table after they lost 2-0 to Leeds United at Elland Road.
Scotland striker Ross McCormack scored twice in the second half for Leeds, who climbed to eighth, just three points off the play-offs.
Birmingham City dropped into the bottom three after a 1-0 home loss to Charlton Athletic, while Doncaster's struggles continued as they were beaten 3-1 at home by Brighton and Hove Albion.
Other results on Saturday saw Bolton win 2-0 at Bournemouth and Wigan Athletic also triumph, edging Huddersfield Town 2-1.
