Ian Maatsen scored two goals in the first half to lead to a 2-1 win for the visitors at the Liberty Stadium.
A free-kick and a drive from outside the box gave the Clarets a 2-0 lead.
There were some good moments for theSwansea side.
In the second half, they missed opportunities to extend their lead.
Their 10th win in 11 league matches gave them a six-point lead at the top of the table.
There is a gap of 14 points between the third- and fourth-place teams.
Russell Martin's team dropped to 14th after their third defeat in a row.
The men arrived in Wales in a good mood after beating the Potters. Their eight-game winless streak came to an end on the same night as the thumping victory overWatford.
The first attempt of the game produced the opening goal for the Clarets.
After the livewire Nathan Tella was tripped by Harry Darling, the whipped free-kick flew beyond Steven Benda and bounced in off the far post.
The hosts almost responded, with Cooper feeding Liam Cullen for a shot which was beaten away by Muric.
Tella danced off the right flank before squaring for Maatsen.
The on-loan left-back hit a fierce shot from outside the box which flew through Benda and into the net.
After Jay Fulton's drive was parried by Muric and Cooper arrived first to sweep in the rebound,Swansea hit back and were able to get back into the game.
Cooper had a chance to score before the break, but his shot was picked out by Allen.
Josh Brownhill wasted two chances to extend the lead in the second period, but it was worth it.
When Brownhill went through on the goalkeeper, first Benda saved brilliantly, then he lifted a second chance over the bar.
Jay Rodriguez missed a big chance when he headed wide after Tella's cross.
There was a scare for the visitors in the last minute of the game when Ntcham was sent on by Congreve, but he missed the target.
All Rights Reserved © 2024
