It was the night all the nerves vanished into the ether, replaced by every track on the Leeds United soundtrack as Premier League survival was all but confirmed. It was all too easy to defeat rudderless and relegated Burnley, to put Leeds nine points clear of the relegation zone, with their rivals having four games remaining.

Anton Stach’s smart shot started the festivities before Noah Okafor and Dominic Calvert-Lewin provided the headline act to move Leeds above Newcastle into 14th and extend the gap to 18th-placed Tottenham. The final half an hour at Elland Road was boisterous as the supporters celebrated a crucial victory in a hard-fought journey to safety.

“We will just celebrate once it is mathematically done but 43 points is good but I don’t just want to settle for 43 points, we want to win the following nine,” Daniel Farke said.

“A massive win for us and the first goal in such a pressure game [is important]. You are still nervous until you score the second and third. It was important to stay with the foot on the gas in the second half.”

Mike Jackson, a man who screams caretaker rather than interim, was back in temporary charge of Burnley for a second time after Scott Parker’s exit on Thursday. Where others might embrace the opportunity to shake things up, he was more conservative, sticking with five at the back in an attempt to keep things tight. These two clubs both reached 100 points last season, with Leeds pipping Burnley to the Championship title on goal difference. There has, however, been a vast gap between them this time round, with Burnley unable to compete at the highest level, sitting on half their opponents’ points tally at kick-off. Leeds recruited smartly, while only Martin Dubravka of the summer arrivals at Burnley can claim to have succeeded.

The goalkeeper, however, will be upset that he reacted slowly and went down like a sack of potatoes when Stach surprisingly decided to shoot from 25 yards. It was a relatively clean strike but lacked ferocity, not that it mattered and the ball found the corner while Dubravka flailed. The goal brought the anticipated euphoria on a night that could reaffirm another year of grand occasions at Elland Road.

Leeds were in control, as Burnley happily sat off. Okafor was the most dynamic outlet when Leeds wanted to speed things up, as the Swiss winger repeatedly tested whether Kyle Walker’s pace was still sufficient to ward off danger, while Stach almost had a second but his jab at the end of some pinball in the area was blocked by Quilindschy Hartman, who was lying on the floor.

For all their control of the ball, penetrating the Burnley backline was proving difficult for Leeds. A few crosses were scrambled away but Dubravka was only once more called into action before the break when a clearance rebounded towards him, not that Leeds had anything to worry about as Burnley failed to muster a single shot on target in the first half.

Leeds needed to sharpen up to find a second goal which would almost certainly end the contest. After a few false dawns at the start of the second half, Calvert-Lewin showed his worth as a provider, driving Leeds up the pitch before a sublime backheel opened up space for Jayden Bogle, who found Okafor at the back post, with Walker only able to watch his heels as he smashed home to provide the perfect end to a fine move.

“We are staying up” and a plethora of other chants were soon reverberating around the ground when Calvert-Lewin reacted quickest to jab home after Dubravka palmed an Ao Tanaka shot straight to the striker. Even the pessimists lost their doubts at the third going in, turning the event into more of a party than a football match in the stands.

Burnley finally woke up, having a Lucas Pires goal ruled out for an excruciatingly tight offside. That was quickly forgotten when Loum Tchaouna smashed the ball legally into the corner.

“It’s been a shock to the group, with Scott leaving and the relationship he had with players,” Jackson said. “The biggest thing for me as a team and a group, we cannot wait for the game to go against us and get going. That has been the situation for a while now.”

The comeback was improbable for a Burnley side that have now won once in their past 26 games. Their summer looks full of uncertainties as they seek a new manager and will likely lose key players before starting life back in the Championship.

Leeds, meanwhile, sit proudly on 43 points, more than the highest tally with which a team has ever been relegated from the Premier League. No one will stop Leeds from marching on in the top flight for another season. “The main objective is to stay in this league and doing so will be an amazing achievement,” Farke said, and he is very close to completing the job.