Frank de Boer's short reign at Crystal Palace was plunged into further turmoil after an early blunder from Lee Chung-Yong brought their fourth straight Premier League defeat.
Burnley new boy Chris Wood pounced on Lee's dreadful backpass to put his side in front with less than three minutes gone, and the hosts held out to leave De Boer's job hanging by a thread after a 1-0 loss.
Palace perhaps deserved something from a hugely-improved performance and should have got it when Scott Dann headed wide from point-blank range in injury time, but that may not be enough to save De Boer.
The manager had made three changes and reluctantly switched to a 4-4-2 formation in a bid to kick-start the season, but looked on aghast as Lee's early error piled on more pressure.
In no danger wide on the left, Lee turned and played the ball back in the direction of goalkeeper Wayne Hennessey, oblivious to the lurking Wood.
And the New Zealand international reacted clinically, firing past Hennessey first time from outside the box to give his side a dream start.
The visitors refused to buckle and were almost level within a minute when Dann took aim from the right side of the box and his shot was cleared off the line by Matthew Lowton.
Two minutes later Palace came close again when the lively Andros Townsend lofted a delicious pass to Christian Benteke, who steered his header inches wide of the far post.
Palace continued to press well, but clear chances were few and far between with the home defence coping admirably with what the Eagles could throw at them.
Burnley suffered a setback just past the half-hour mark when Heaton was forced off with a shoulder injury after landing awkwardly, meaning a Premier League debut for 25-year-old Nick Pope.
However Palace failed to pressure the new boy, whose only act in low-key ending to the first period was a good low save to deny Townsend.
The second half began in much the same vein, with Palace pressing to little effect, their best early opportunity falling to captain Jason Puncheon who drilled a half-chance wide.
The Londoners had two chances in the 71st minute, substitute Levi Lumeka just beaten to a Townsend cross by Lowton before Jeffrey Schlupp blazed a fine chance over from the middle of the box.
But the home side came even closer two minutes later, when substitute Ashley Barnes drifted in from the right flank and unleashed a low, curling effort which was superbly kept out by the diving Hennessey.
Benteke was denied by the advancing Pope in the 78th minute then Dann missed to ensure another dismal afternoon for De Boer and Palace.