The Yorkshire derby was, as expected, a tight game in which both sides created good chances to score. Leeds goalkeeper Illan Meslier made a couple of huge saves in the first half and the visitors were indebted to the young Frenchman as they went in at the break goalless.
Leeds began to look more threatening as the second half wore on and eventually, in the 88th minute, got a breakthrough when Jack Harrison's cross was nodded in by Patrick Bamford for his third goal in three Premier League games.
Bielsa admitted it was a tight game and his side could have found themselves coming out for the second half trying to get back into it. Ultimately, however, he felt the result was the right one.
"It was very even," said the Argentine after his second top flight win.
"We could've gone ahead but we could've also gone in at half-time behind. In the second half we were better - we dominated more with more opportunities.
"I think the result in the end was a just one."
To Bielsa it appeared that nothing about the way Leeds operated changed after the second half, but the energy with which they went about their work made a difference.
"We tried to do the same things that we did in the first half but we added extra energy to it," he said.
"It's always hard to tell whether it is because the opponent is worn out a little or we're putting in extra effort. I have the sensation that we continued to play the same way but we found a way to build our attacks easier. There were individual actions we found which caused an unbalance in the opponent."