Leeds celebrated Premier League safety as Jack Harrison's 94th-minute strike gave them a 2-1 win at Brentford to escape the bottom three at Burnley's expense.
Harrison's late goal sparked wild scenes among the away fans as Burnley dropped into the bottom three.
Knowing they needed to better the Clarets' result owing to their vastly inferior goal difference, the pressure of their challenge weighed heavy on Leeds early on.
- How the teams lined up | Match stats
- Sunday's scores | Premier League table
- Get NOW to stream big moments | Get Sky Sports
Once they settled into the game they looked relatively comfortable against a Brentford side lacking sharpness and on a chaotic afternoon across the Premier League, moments after news filtered through that Newcastle were leading at Turf Moor they thought they had taken the lead themselves through Joe Gelhardt, only for a VAR review to deny them the opener.
Bryan Mbeumo missed presentable opportunities in either half for the hosts before a rare David Raya howler saw him scuff a pass straight to Rodrigo, who he then bundled over in the box. From 12 yards, Raphinha stepped up to send him the wrong way and leave Leeds within touching distance of safety.
That survival bid was given another helping hand when Kristoffer Ajer was forced off injured after Brentford had used all three substitutes, but they still reignited Leeds' sense of angst as Sergi Canos nodded home Josh Dasilva's cross to level.
He was booked for his celebrations and was soon shown a second yellow for fouling Raphinha on the halfway line, but still Leeds could not re-establish their advantage until Harrison's long-range deflected effort beat Raya in the fourth minute of injury time to guarantee their survival.
Leeds leave it late - again - to breathe easy
It wasn't until Harrison's last-gasp winner that Leeds' capacity travelling support could finally celebrate in the knowledge that they had a third consecutive season of Premier League football to look forward to.
In the end, it wasn't quality that told but a never-say-die attitude which has underpinned Leeds' survival far more than anything else.
Harrison's goal was their fourth 90th-minute winner of the season, a tally no-one across the Premier League can match. It should have been an easier afternoon for Marsch's side, who were handed a glorious chance for the opener through Raya's mistake and then should have seen out victory when Ajer was forced off injured.
But they had struggled to create in open play all afternoon, and even with a man advantage their fate appeared perilous when Canos nodded in Dasilva's cross and the knowledge one Burnley goal at Turf Moor would be enough to send them down.
Even when Brentford were reduced to nine men, Raya's goal rarely appeared in serious danger until Dasilva's clearance from a last-minute corner fell for Harrison, whose 25-yard effort took a slight deflection to beat the goalkeeper inside his near post.
This may be the way Leeds have operated in recent times, but it is not a formula Marsch wants to continue.
"I've heard this a lot about Leeds United, that we think we have to do it the hard way," he said after the game. "Part of my job is to change that mentality, to say we deserve more, that we have an incredible club and team, and honestly I think it's not by accident we've scored four winners or equalisers in injury time.
"We've had belief, but we've had to earn it. I've heard this is the Leeds way, but I'm not buying into that."
Pride for Brentford despite final-day defeat
A top-10 finish was the carrot for Brentford at the end of a season where they have achieved Premier League safety with relative ease, but having retained their momentum into the final weekend courtesy of back-to-back wins, they looked out of sorts across 90 minutes and failed to turn spells of first-half domination into anything more concrete.
Mbeumo's two efforts aside, narrowly missing the far post when played through before the break and firing straight at Ilian Meslier moments after the restart, Canos' goal was as much as they could muster against a Leeds side with the second-worst defence in the Premier League.
Despite their underwhelming afternoon in West London, they were cheered off at the full-time whistle by the home support more than content to focus on a season where they have defied the critics and become the only one of last year's three promoted sides to remain in the division.
Christian Eriksen's arrival in January has proven a major catalyst in that achievement, and after the game said: "To be disappointed in the last game to lose is something to build up. We have been on a good run and after a few hours I think everyone will settle down and be in good mood.
"I was just happy to be back playing. To be the normal me and to play football in the Premier League again. To come back and help them stay up, I am very proud of that. It is different from where I have been before but to be here now having played good football in the last six months, I am very pleased.
"On the last day of the season, to bring your family on to the pitch, it is special. Now it is a week off and then with the national team, so a few games still to go. But first a holiday."