A week after their loss, by the same scoreline, to the champions Liverpool, the Whites engaged in another madcap game against their fellow top flight newboys.
At 4-1 up in the second half they had the visitors right where they wanted them, only to ship two goals to make things a lot more tense than they needed to be.
Ultimately, Leeds are on the board however and from an entertainment point of view have been terrific value in their first pair of outings.
"It was a game where we couldn't really show ourselves," said Bielsa.
"In the first half we defended better but we didn't really create much danger. In the second half we attacked a bit better but we didn't finish attacks very well. Finally we were able to impose our game a little bit."
In a complete change from the Leeds United who won the Championship, the team has not been able to show the defensive solidity that made them so difficult to score against, while scoring freely themselves. In Bielsa's first two seasons they struggled to make the most of the many opportunities they created.
It's too early to start seeing trends, in the Argentine's opinion.
"There's no particular motive for us being so efficient at the moment," he said.
"Normally we are a team who need a lot of chances to score goals, at the moment the opposite is happening. I don't think there's anything definitive behind this.
"We've only played two games. Nothing that happens can be called a tendency at the moment. We will have to wait a few more games before we can start making conclusions."
That's not to say he's not concerned about the seven goals Leeds have conceded in two Premier League games. Yet he's confident they can resolve whatever issues they're having at the back.
"We are worried," he said.
"It's not like things that we don't expect to happen are happening. The goals we have conceded, there has been nothing surprising. Anyway, as the competition goes on I think we will be able to improve our defensive performance. We will identify why these errors happened and prevent these difficulties from happening again."
What Bielsa did find comforting was the way in which Leeds managed to keep Fulham at bay late on at Elland Road, after coming under intense pressure as the scoreline moved from 4-1 to 4-3. The way the final stages played out, with Leeds spending plenty of time high up the pitch and winning free-kicks deep in Fulham territory, was proof for Bielsa that attack is still the best form of defence for this team.
"In this game what I liked a lot is the way we were able to manage the game when we were only one goal ahead," he said.
" After the two goals we conceded in a short period of time and the shot that hit the post we were able to defend well and attack. That period, that last 20, 25 minutes were the best thing about this game.
"What the match showed was that we need to continue to do the things that made us successful in the first place rather than putting players behind the ball. It's an error to think you should stop doing the things which have made you successful once you're leading."
Leeds were without Pablo Hernandez who suffered a groin injury in the warm-up, while Kiko Casilla didn't make the bench after picking up a knock in the midweek Carabao Cup loss to Hull.
Rodrigo got his first Premier League start for his new club in Hernandez' place but was withdrawn at half-time by Bielsa.
"Pablo had a small knock in the warm up," said Bielsa.
"We don't think it's very serious. With regards to Rodrigo it was a tactical change. He did a very good game against Hull from a physical standpoint. I talk from a physical standpoint because from a football standpoint the whole team didn't play well against Hull. I thought that if he could replicate that physical performance against Hull today we could have created a lot of danger against Fulham.
"I was under the impression that he lacked a bit of energy to be able to show his capabilities. I think that has something to do with the physical effort he used against Hull. That's why I decided to sub him. Anyway, from a physical standpoint it was a very hard game for our attackers."