Danny Dichio's 69th minute headed goal, his sixth in five games, helped Millwall win a fractious FA Cup fifth round tie, and secure a place in the last eight.
However, Burnley will be looking back at several missed chances that could have won them a replay, while Millwall will know they could have had more goals themselves.
In truth, had the sides ended up sharing half a dozen goals, nobody would have been in the slightest bit surprised.
Richard Chaplow's looping header in the second minute almost gave Burnley the perfect start. The ball drifted fractionally beyond the far post as Millwall keeper Willy Gueret had his blushes spared, as he stood stranded.
An incident after 13 minutes proved to be one of the main talking points. It added an injection of malice into proceedings which was to last through the course of the contest.
Referee Howard Webb, his linesman and most of the crowd failed to see exactly what happened off the ball between Kevin Muscat and Ian Moore, but Muscat was left prone, holding his face, as a mass brawl was narrowly averted.
With tackles flying and tempers flaring, Burnley enjoyed marginally the better of the opening period, although had keeper Brian Jensen not reacted in acrobatic style in the 18th minute to deny Paul Ifill's fine left-footed volley, the home side would have claimed the lead in dramatic style.
Minutes later, Ian Moore's fine run down the right flank saw the Millwall defence beaten for pace, and had his low cross, having been fumbled by Gueret, found a Burnley boot rather than being cleared to safety, it would have been little more than Stan Ternent's side deserved.
As it was, the home side were left rueing two glaring misses from new signing Dichio, who planted a header over the bar when perfectly placed, before somehow failing to send the ball home from six yards out as it broke sharply to him from a corner.
Gueret redeemed himself just before the break, saving well from Ian Moore after another surging charge, leaving the sides deadlocked but equally aware that both had enjoyed enough chances to be comfortably ahead.
The second half started in as bad-tempered a fashion as the first had ended, with Dennis Wise booked for an elbow on Tony Grant, and Neil Wood also entering the notebook for a retaliatory lunge on Wise.
Ifill's spectacular drive rebounded off the Burnley bar in a rare moment when the football overcame the niggles, but in general the game had descended into a bad-tempered scuffle, destined to be won by a mistake or a moment of inspiration.
Thankfully, it was the latter, as Muscat's 69th minute right-wing cross swerved into the area to be met by the head of Dichio, who made no mistake with the inch-perfect offering from six yards.
Two minutes later, and Millwall's task was made easier by the sending off of Paul Weller for lashing out at Wise, having come on as a substitute just 12 minutes earlier.
Burnley still had a golden chance to take the game to a replay however, only for Alan Moore to fail to connect with a header, when confronted with an open goal.
For Millwall's assistant boss Ray Wilkins, it was a throwback to great cup clashes of the past.
"That was hectic stuff at the end there, but when you don't retain the ball you're going to end up under a bit of pressure," he said.
"It's a blokes' game though, and there's no point moaning about it, even though I hated it as a player, because that's what makes a great cup tie.
"As long as we're at home in the next round, I don't mind who we get. No, actually, I'd rather get Tranmere than Arsenal!" Stan Ternent was disappointed yet honest about the day's events.
"We had chances, but we didn't take them and Millwall did. It was a proper cup tie, so good luck to them, and I hope they go a long way." Man of the match: Paul Ifill – Unlucky when his brilliant shot came back off the crossbar but was behind most of Millwall's best moments.