On a day when Leeds paid tribute to club great Jack Charlton, Marcelo Bielsa's side moved to within four points of ending their 16-year wait to play in the top flight of English football.
Bielsa felt Leeds had taken a "step forward" to winning promotion after Pablo Hernandez's late winner secured a 1-0 victory at Swansea.
They now sit three points ahead of second-placed West Brom, and six clear of in-form Brentford, with games against Barnsley, Derby and Charlton to come.
On an day when the clubs fans couldn't, of course, share in the afternoon's emotion, Leeds warmed up wearing t-shirts with 'RIP Big Jack' written on the front.
Both sides then paused for a minute's silence followed by an applause before kick-off.
The contest looked destined to end in a goalless draw until Spaniard Hernandez bagged an 89th-minute winner.
Afterwards, Bielsa refused to countenance how close his job is to being done.
"I can not enjoy this," Bielsa said. "What you feel just is that you are taking a step forward. The only thing I can enjoy is the last objective, if we get it.
"The match was very close, very narrow, few chances. When the match progressed our possibilities were growing and in the last 30 minutes I think we deserved to score and to make the difference."
In a game of few chances prior to substitute Hernandez's late strike, Leeds had the best opportunity after 64 minutes.
Patrick Bamford failed to head home from six yards, allowing Swansea goalkeeper Freddie Woodman to palm away his effort.
But Hernandez, who played for Swansea for two years between 2012 and 2014, proved the hero by rolling home Luke Ayling's cross off a post.
"What we feel is taking the steps we have to take," Bielsa said.
"But of course when you score at the end of the match it's a higher feeling. The bigger emotion we didn't get that yet."
Tributes were paid to Charlton before kick-off with both sets of players and staff applauding the former defender's contribution to football after a minute's silence had been held.
"The legends of the club deserve a big attention from us," Bielsa said.
"But I don't want to take the risk to talk about the victory and the loss of a person. I don't want to link those two things."
But matchwinner Hernandez is certain the club's record appearance holder will be with the Whites in spirit for their final three games.
"We received the bad news the other day but I think everyone within Leeds United and all of the fans remember him.
"He is part of the history of this club and I think these three points are for everybody and for the fans but especially for him and for his memory.
"I am sure he will help us in the next week's games from the sky and this win is for him."
Woodman (Mulder 90), Naughton, Cabango, Guehi (Celina 90), Roberts, Fulton (Byers 90), Grimes, Bidwell (Cullen 90), Gallagher, Ayew, Brewster (Routledge 81).
Meslier, Ayling, White, Cooper, Dallas (Alioski 46), Phillips, Helder Costa (Shackleton 90), Klich, Roberts (Hernandez 46), Harrison (Berardi 90), Bamford.
Keith Stroud (Hampshire).