It was a rare show of affection from the Whites head coach, whose celebrations of goals is ordinarily relatively conservative and almost always done individually. As James secured the victory for Leeds, Bielsa turned to hug Quiroga tightly in the technical area.
The importance of Daniel James' late headed goal, which added to strikes from Jack Harrison and Stuart Dallas, was felt keenly by the Argentine.
"It was very necessary to get the win and it was a relief for us to be able to get it," he said after his side opened up an eight-point lead on the Clarets, who occupy 18th place in the Premier League table.
"Of course I don't ignore the situation that we're in and I don't ignore what my responsibilities are, that can't not influence my state of mood."
The result and the scoreline were deserved, he felt.
"We managed a fair victory," said Bielsa.
"The difference I thought was also fair. It's very difficult to play against Burnley. They have it very clear how they want to play and they always keep the differences close.
"What we were trying to do was recover the best way we know how to play and in some ways we got it.
"As you well know in football you have to prove yourself. Even if the performance today was good we have to maintain that level of performance against any opponent and on any pitch."
Leeds were able to exploit mistakes and space in the Burnley half of the pitch in the first half and looked to hit their visitors on the break in the second, which brought a much more even contest.
Burnley substitute Maxwell Cornet cancelled out Harrison's opener nine minutes after the interval and gave Burnley a much more potent look up front, but Leeds' quality eventually told.
"In some way we managed to get in behind," said Bielsa.
"There was a lot of combination play, there was a defensive security even if it wasn't absolute. We had the ball a lot of the time. We managed to finish our attacks in the opponent's half.
"Gelhardt coming on for Tyler maintained the game how we wanted it. Down the left James opened up paths and ended up scoring.
"We dominated the game, created danger, they created not too much danger against us, but the game was very difficult to sustain. They managed to make it very difficult.
"I thought it was going to be difficult to go again [after Burnley’s goal] but we managed to get back and dominate the game again. We played a lot like how I want us to play."
All three of Leeds' goals sparked wild celebrations inside Elland Road but each of Leeds' goalscorers wore their hearts on their sleeves when the ball hit the net. For Harrison it was a first Premier League goal of the season. Dallas' screamer marked his 250th Leeds appearance for the club. The Ulsterman has had a difficult season, suffering a personal tragedy and contracting Covid-19, but looked back to his best against Burnley. As for James, end product has been a struggle since his big-money move from Manchester United, and the goal secured a huge victory for Leeds.
"Harrison needs to progressively get back to his best level," said Bielsa.
"To score a goal is always an impulse to get to that objective.
"The game today was a game of a lot of commitment. To have scored a goal that would allow us to establish differences, it was an important emotion and evidently Dallas needed to express it."