Brian Laws' homecoming party was spoiled by a late goal from John Terry which kept the England captain on the back pages as well as the front of the national newspapers.
Terry went into the game at the eye of a tabloid storm over his private life and faced further disappointment as battling Burnley threatened to upset Chelsea's title challenge.
Steven Fletcher's superb 50th-minute goal looked set to give the Clarets a valuable point in their survival scrap in Laws' first home game as Burnley boss as the Scot cancelled out Nicolas Anelka's first-half strike.
But Terry headed home seven minutes from the end to take his side temporarily four points clear at the top of the table and leave Burnley in the bottom three.
It meant a fourth straight league defeat for Burnley and only a second loss at home all season.
But the Clarets didn't go down without a fight as they ended their long goal drought and, with potentially less demanding fixtures to come, restored belief that they can win their survival scrap under Laws.
Steven Fletcher celebrates his equaliser
The former Burnley defender was given a fantastic reception as he made his way across Turf Moor before kick-off, while his presence was also apparent on the team sheet as new signing Leon Cort was given his debut following his signing from Stoke City.
Cort partnered Clarke Carlisle in the centre of defence with Carlisle taking on the captain's arm band in the absence of both Steven Caldwell and Graham Alexander.
With Alexander and Chris McCann both failing to recover from injuries picked up in mid-week, the return of Andre Bikey from international duty was a timely one as he slotted into midfield alongside Kevin McDonald.
And Laws couldn't have asked for much more fom his side in the opening stages as Cort played his part in drawing Chelsea's early sting.
The Clarets then started to take the game to the league leaders with Chris Eagles, Robbie Blake and Steven Fletcher asking questions of the Blues' defence.
But just when Burnley were looking to build up the momentum they fell behind to a lightning Chelsea break-away.
John Terry clears under pressure from Fletcher
The Clarets were caught short at the back when a free-kick came to nothing and Chelsea goalkeeper Petr Cech instantly turned defence into attack with a quick throw to Joe Cole on half-way.
The England winger advanced and delivered a cross-field ball for Florent Malouda who knocked it inside for Anelka to sweep home his sixth goal in as many games.
The goal came as a body blow but Burnley responded well and Wade Elliott, having his best game for a number of weeks, rolled in a low cross which was cleared for Bikey to let fly with a shot which failed to worry Cech.
John Terry was booked for blocking off Blake as he looked to run onto Fletcher's flick and Eagles tried to fashion a couple of openings around the edge of the penalty area.
But Chelsea don't boast the best defensive record in the league for nothing as they continued to make life hard for the Clarets, who were forced into a further defensive change ten minutes before the break as David Edgar replaced the injured Christian Kalvenes at left-back.
Andre Bikey stops Joe Cole in full flight
Yet as Laws has been preaching, if his side tightens up to concede fewer goals and stay in contention in games they will have a chance and five minutes into the second half the Clarets were level thanks to a bit of magic from Fletcher.
The Scot's first touch from Blake's nicely flighted pass was sublime to wrong-foot Alex who could only hook the ball against Fletcher who pounced to drill an angled left foot shot past Cech.
Burnley's first league goal of the year had Turf Moor bouncing and with confidence restored Laws' men suddenly looked more dangerous every time they went forward.
But the equaliser also sparked Chelsea into life. Sensing the potential loss of points in their title push, the Blues launched their most penetrative spell of the match and Frank Lampard and Michael Ballack both saw shots bravely blocked by Cort and Kevin McDonald before Joe Cole had a header ruled out for off-side.
That was a tight call and Lampard, who previously carried little threat, then fired in a free-kick which Jensen saved low to his right.
Burnley defended for their lives, typified by a magnificent block from Carlisle as Ashley Cole bore down on goal and a save by Jensen to thwart substitute Daniel Sturridge.
But from the corner that followed Chelsea grabbed the winner. Lampard delivered and Terry was left with too much space to send a downward header into the bottom corner and leave Burnley's courageous efforts counting for nought.
Burnley: Jensen, Mears, Kalvenes (Edgar 35), Carlisle, Cort, Bikey, McDonald (Paterson 60), Eagles, Blake (Thompson 71), Fletcher, Elliott. Substitutes: Duff, Gudjonsson, Nimani, Weaver.
Chelsea: Cech, Ivanovic, A Cole (Deco 76), Lampard, J Cole (Sturridge 71), Ballack, Malouda, Zhirkov, Terry, Alex, Anelka. Substitutes: Turnbull, Carvalho, Ferreira, Matic, Borini.
Referee: Phil Dowd
Coming through: Kevin McDonald