Victor Moses was the match-winner as Chelsea eased the pressure on London rivals Arsenal by denting Burnley's surge for sixth place.
The Clarets kicked off at Turf Moor on the back of a five-match winning run, knowing a sixth would see them leapfrog the Gunners and bring the prospect of guaranteed Europa League football within touching distance.
But Moses produced the first-half cross which spawned Kevin Long's own-goal then drilled home a decisive low shot to make it 2-1 after Ashley Barnes had equalised by unintentionally deflecting a Johann Berg Gudmundsson shot.
Burnley, whose stellar season began with an opening day victory at Stamford Bridge, still have a chance to see more regular Thursday night football by finishing seventh, while three points ensured the Blues had fair reason to toast Antonio Conte's 100th game in charge.
Alvaro Morata looked unlikely to join in any celebrations though, missing a sitter at 1-0 and fuming when he was replaced by Eden Hazard.
Conte, three days before his side's FA Cup semi-final, made six changes from the side which beat Southampton at the weekend
There was a starting shirt for Olivier Giroud, and with it the chance to break the super-sub mould which has followed him from Arsenal, and a first Premier League start for Emerson Palmieri.
The £17.5million signing from Roma has been kept to just 105 minutes since his January arrival and was quick to shake off the cobwebs with a handful of testing crosses from the left wing-back slot.
Chelsea's old-fashioned front two of Giroud and Morata were also into the game early, the Frenchman with an early penalty appeal against Long and Morata denied by Nick Pope at the near post.
Burnley's resistance lasted 20 minutes but broke when Gary Cahill's long ball from defence found Moses on the charge.
He cushioned the ball on his chest, shook off Stephen Ward and pinged a cross into the six-yard box.
Pope failed to intercept and Long, mindful of Giroud lurking over his shoulder, bundled untidily into his own net.
The hosts briefly threatened to fight their way back into the game on the half-hour, but a period of prolonged adventure yielded nothing more than a half-chance for Barnes.
It was much the same story for the first 10 minutes of the second half, the Clarets winning the battle for territory but failing to test Thibaut Courtois.
Having absorbed the pressure, N'Golo Kante set Chelsea off on a classic counter-attack by sweeping the ball directly into the path of the Morata on halfway.
The Spaniard sped towards goal with neat control, gave Pope the eyes as he moved into the box and then slotted a couple of inches wide from eight yards.
Nobody on the pitch looked more surprised than the Spain striker as the ball cannoned back off an advertising board rather than nestling in Burnley's net.
Burnley's good fortune only increased in the 64th minute when they drew level courtesy of an unwitting Barnes.
He attempted to jump over Gudmundsson's low shot but mis-timed his leap and saw the ball skip past Courtois via a deflection from his heel.
The visitors restored order inside five minutes, Emerson stinging Pope's palms then feeding Moses on the right of goal.
After sizing up his options he rifled a low effort at the near post, beating Pope for pace.
Morata was replaced by Eden Hazard moments later, reacting angrily to his exit but perhaps blaming himself more than his manager.