The game at Portman Road seemed to be drifting towards a goalless draw until Burnley's Scott Arfield headed home Kieran Trippier's 80th-minute cross to seal a sixth straight league win for Sean Dyche's side.
Second-placed QPR looked like joining Burnley on 29 points until Millwall grabbed an injury-time equaliser to secure a 2-2 draw at The Den.
Dynamo Kiev loanee Niko Kranjcar put Harry Redknapp's side ahead with his first QPR goal before Scott McDonald levelled shortly after half-time.
It looked as though the visitors had done enough to take all three points after Charlie Austin put them back in front but Jermaine Easter struck two minutes in to added time to give the Lions a share of the spoils.
Leicester moved to within a point of QPR after seeing off 10-man Huddersfield 2-1 at the King Power Stadium..
Jamie Vardy converted Dave Nugent's pass on 11 minutes to put the hosts ahead before an Anthony Gerrard own goal doubled their advantage before half-time.
Paul Konchesky then put past his own goalkeeper to give Huddersfield hope but they could not find an equaliser and saw top goalscorer James Vaughan sent off late on.
The Foxes' east Midlands rivals Nottingham Forest remain fourth in the table but lost ground after a dramatic equaliser from Bournemouth at the City Ground.
Henri Lansbury's sumptuous finish, his third goal in two games, looked to have been enough for Forest before Marc Pugh struck from the edge of the penalty area in injury time to secure a 1-1 draw for Eddie Howe's Cherries.
Blackpool did not miss manager Paul Ince, who served the first of his five-game stadium ban, as his son Tom scored the only goal of the early kick-off from the penalty spot as they beat Wigan 1-0.
Scott Carson brought down Newcastle loanee Dan Gosling with Ince making no mistake from the spot and Wigan's day was made worse in the last minute as James McClean was sent off.
Steve McClaren made it two wins from two as Derby manager following a 3-2 win at promotion hopefuls Watford.
Jamie Ward struck a first-half brace either side of Fernando Forestieri's effort to put the Rams ahead at the break.
Lewis McGugan drew Watford level once more but Conor Sammon's 88th-minute goal proved to be enough to give Derby the win.
Reading leapfrogged Watford in to sixth place with a comfortable 4-1 home win against Doncaster.
Theo Robinson had levelled for the visitors after Danny Guthrie put the Royals in front but goals from Adam Le Fondre, Garath McCleary and Pavel Pogrebnyak sealed the points for Nigel Adkins' side.
Barnsley moved off the foot of the table with a 3-2 home win over Middlesbrough.
Goals from Paddy McCourt and a double from Chris O'Grady, the second of which was a penalty, had put Barnsley 3-0 up at half-time.
But the Tykes were made to sweat late on as Albert Adomah struck twice in two minutes but the visitors ultimately fell short.
A seventh-minute goal from Simon Church was enough for Charlton to pull themselves out of the relegation zone with a 1-0 win at Blackburn.
Fellow strugglers Bolton and Sheffield Wednesday shared a point following a 1-1 draw at the Reebok Stadium.
Jermaine Beckford put the hosts in front before an unfortunate own goal from Alex Baptiste drew Wednesday level before the break.
No-one could find a winning goal and the visitors were left hanging on in the final five minutes after Jose Semedo was sent off.
Yeovil remain bottom but will be lifted by a good performance that saw them hold Brighton to a 0-0 draw at Huish Park.