On the hottest October day on record, the Clarets kept their cool to keep the Lions of Millwall at bay and record their second away win of the campaign thanks to a first clean sheet since March.
Jay Rodriguez's eighth goal of the season at the ground where he scored his first career goal away from home almost a year ago to the day was enough to give Eddie Howe's men back-to-back Championship wins for the first time this season.
But it took an heroic rearguard action to secure the points as Burnley battened down the hatches in the second half to secure a first shut-out in 24 attempts.
The last came at Hull City, a week before Millwall won 3-0 at Turf Moor to start the rot.
The Lions don't find scoring goals so easy these days with just seven in the Championship so far.
But they threw everything at Burnley in an effort to cancel out Rodriguez's 38th-minute strike and it took some sterling performances from the back four and goalkeeper Lee Grant to set up a win that adds real momentum to the Clarets' campaign.
Jay Rodriguez celebrates the winner
In the sweltering conditions the first half produced much perspiration but little inspiration as neither side was able to grab the initiative until the Clarets struck eight minutes before the break.
Millwall's greatest threat had come inside the first minute when a long kick from goalkeeper David Forde - a weapon the home side looked to utilise as often as possible - bounced all the way through towards opposite number Grant.
Under pressure from Danny N'Guessan, the Clarets' keeper had to punch away at the expense of gashed chin following a clash in mid-air.
That apart the Lions showed plenty of energy but looked like a side bereft of goals, while Burnley's invention invariably broke down in the final third.
Rodriguez and Ross Wallace led a couple of dangerous break-aways that came to nothing and Junior Stanislas used his pace to great effect when beating Paul Robinson to a Chris McCann through-ball before just failing to pick out Rodriguez.
Lee Grant leads the rearguard action
But the Clarets hadn't really tested Forde until their second corner of the game unlocked the Lions' defence to earn them a lead.
Rodriguez, buoyed by his first Championship goal of the season in mid-week and looking full of running, had the confidence to try his luck from Wallace's corner which had been played behind the decoy run of David Edgar.
The striker's effort from the edge of the box lacked pace but not direction and with Forde scrambling across his goal, the ball beat him into the bottom right-hand corner.
Millwall boss Kenny Jackett responded by sending on John Marquis in an effort to beef up the Lions' attack and his presence did liven up the home side as they made a positive start to the second half.
Marquis was flagged for off-side before putting the ball in the net and Brian Howard forced Grant into a save from a long-range free-kick as the Clarets were put under sustained pressure for the first time.
Charlie Austin mucks in at the back
A second goal would have taken the sting out of the situation but Burnley didn't keep the ball long enough to create more than one decent opening for Stanislas, who curled his effort wide of the far post after being played in by McCann.
Grant was forced to make another smart save to turn away a Liam Feeney volley and the Clarets must have held their collective breath when Marquis went down in the penalty area under a challenge from Edgar, with referee Simon Hooper giving the verdict Burnley's way and booking the Millwall man for diving.
Howe sent on both Dean Marney and Keith Treacy to provide some fresh legs and dropped Rodriguez deeper to try and stem the flow but it was desperate stuff at times as Hamer Bouzza whistled one over the top and Marquis looked a certain scorer until his goalbound header was superbly saved by Grant with the help of Edgar who completed the block.
Eddie Howe applauds the Clarets' fans
Brian Easton went into the book for time wasting and play was held up for a short moment as Kieran Trippier had a plastic bottle thrown at him as he waited to take a throw-in.
But among the mayhem the Clarets held out and after surviving four minutes of added time signed off in perfect style for the latest international break as they celebrated with a show of unity in an on-pitch huddle in front of the travelling fans.
Burnley: Grant, Trippier, Easton, Edgar, Amougou, Bartley (Marney 73), McCann, Wallace, Rodriguez, Austin, Stanislas (Treacy 78). Subs: Mee, Hines, Stewart.
Booked: Trippier 45, Bartley 70, Easton 87.
Millwall: Millwall: Forde, Mkandawire, Barron, Robinson, Ward, Trotter, Henry (Bouazza 72), Feeney, Simpson (Marquis ht), N'Guessan, Howard. Subs: Dunne, Abdou, Mildenhall.
Booked: Howard 54
Referee: Simon Hooper
Attendance: 10,460 (574 Burnley)
In it together