The Clarets picked up where they left before the international break with goals from Jack Cork and Ashley Barnes making it three straight wins in the Premier League for the first time.
Sean Dyche’s men also made it a hat-trick of top-flight victories for the first time since January, 1975.
And you have to go back a season before that since the Clarets enjoyed a better start to a campaign as a sixth win took Burnley up to 22 points - still in seventh spot but level with Liverpool, two places higher in the table.
The victory – arguably the most comfortable of the season – also capped a memorable few days for Cork.
Having won his first England cap just over a week ago, the midfielder headed the opening goal against the club that sold him in the summer.
And the quality of Cork’s excellently-constructed effort was then matched by Barnes’ explosive finish as two goals before half-time were enough to keep the Clarets soaring and the Swans struggling as a fourth successive defeat equalled their worst run in the top tier.
With Chris Wood’s hours in the air effectively counting the New Zealand international – who returned from unsucccesful World Cup duty on Friday morning – out of contention, Dyche made one change to the side that had started the win at Southampton, which sent Burnley into the international break on the back of successive victories.
Barnes - who along with goalscorer Sam Vokes had come off the bench to great affect at the St Mary's Stadium - was the one who got the nod to replace Wood.
And the striker again fully vindicated the manager’s decision as the Clarets set about trying to end a losing streak against the Welshmen which ran to four games and six losses from the last seven meetings.
The Swans had twice done the double over Sean Dyche’s men in their Premier League history, but this is now a different Burnley.
And the Clarets showed exactly what they are about in a dominant first-half performance which was among their best at Turf Moor this season and could easily have brought them more than just first league goals of the season from Cork and Barnes.
After a cagey opening 15 minutes the Clarets took a grip as they went hunting for the opening goal.
Steven Defour twice went close to providing it as he nearly punished Lukasz Fabianski for a sloppy clearance and then tested the Poland international with a stinging drive after Johann Berg Gudmundsson had kept the ball alive following Robby Brady’s cross from the opposite flank.
The Clarets were causing havoc down both wings and when Defour sparked another attack, Matt Lowton crossed to the far post where Barnes connected with a header which had the over-worked Fabianski scrambling to save.
Swansea, arriving on the back of five defeats in six games, simply couldn’t cope with Burnley’s pressing and movement and with half an hour gone they were opened up again as Cork made the break-through.
The new England man finished a superb move, which started right back with goalkeeper Nick Pope before Cork got involved for the first time with a dart forward and ball into Barnes, who then laid if off to Brady.
Brady’s cross was inch-perfect and Cork, continuing his run into the box to perfection, nodded past former team-mate Fabianski to claim his first top-flight goal for the Clarets since the end of his first loan spell at Turf Moor in 2009/10 and his second of the season following a League Cup goal at Blackburn Rovers.
Barnes was yet to score in any competition but on just his second league start opened his account in stunning style.
Jeff Hendrick, who liked Brady and Stephen Ward did well in overcoming the disappointment of their own World Cup exits, provided the chance with the ball forward to Barnes after Defour had won back posession on half-way.
But it still needed a blistering strike from 18 yards to send the ball flying past Fabianski to give the Clarets the second goal their dominance had merited six minutes before the break.
In a bid to turn the tide, Swans’ manager Paul Clement replaced Jordan Ayew with Wilfried Bony at the start of the second half and Bony did create a chance for Tammy Abraham, which the England new boy lifted over the bar.
But the Clarets could have been 3-0 up by then with Pope’s clearance bouncing all the way through for Hendrick, whose attempted lob was smothered by Fabianski three minutes after the re-start.
And while Burnley’s superiority was not as apparent in the second 45 minutes, they had done more than enough to put the result beyond doubt.
Happy to play on the break, the Clarets couldn’t conjur up a third goal from a handful of late chances, with James Tarkowski unfortunate to see an effort chalked off for off-side following a corner when the television evidence suggested he was in line with the last defender.
But at the other end there was simply no encouragement for Swansea to sense a comeback as the Burnley back line again closed the game down - epitomised by Lowton's whole-heated double block - as Pope did not have a serious save to make in completing a sixth sheet in nine league games to round off another job very well done.
Burnley: Pope, Lowton, Tarkowski, Mee, Ward, Gudmundsson, Cork, Defour, Brady, Hendrick (Vokes 79), Barnes. Substitutes: Lindegaard, Taylor, Westwood, Wells, Long, Arfield.
Swansea City: Fabianski, Naughton, Fernandez, Mawson, Olsson, Fer (ki 69), Sanches, Clucas, Dyer, Abraham (Narsingh 80), J Ayew (Bony ht). Substitutes: Nordfeldt, Van der Hoorn, Carroll, Routledge.
Referee: Martin Atkinson