The Whites cast aside a poor first-half performance to come from behind and register a key 2-1 success to move three points clear at the top of the table after only their second win in five league matches.
A 2-2 draw between nearest rivals Norwich City and third-placed Sheffield United helped Leeds extend their advantage over the duo with Bielsa’s side now boasting a six-point advantage over the Blades.
Leeds – who host the Canaries in a summit meeting on Saturday – were indebted to a second-half brace from Polish midfielder Mateusz Klich, who ensured the visitors found the net for the 15th successive away game at the start of a second-tier season.
This was something last achieved by Blackburn Rovers back in 1984-85.
Bielsa, whose side took the points courtesy of an 85th-minute winner from Klich, who profited from Millers mistakes for both goals, said: “The game made us think that we could score another goal.
“I do not think Rotherham dominated the first half. We had the ball, but we did not create any danger.
“In the second half this changed. We attacked better and we had chances to score. The first goal had a positive impact on the team. It was a necessary win.
“When it is hard for the team to score goals it is important to have another player (Klich) capable of scoring them. It is always something positive.”
While Leeds’s players and staff celebrated a potentially pivotal moment of their season amid ecstatic scenes at the final whistle there was deep-seated disappointment for Bielsa’s counterpart Paul Warne.
Once more the Millers’ Achilles heel of conceding costly late goals flared up. Their tally of goals against in the final 10 minutes of matches rose to 12 and only Millwall, with 14, have a worse record in the Championship.
The loss meant that Rotherham, two points clear of third-from-bottom Reading – having played a game more – have suffered back-to-back Championship home losses for the first time this season.
Warne, whose side were full value for an interval lead provided by a fantastic long-range strike from Semi Ajayi, said: “The goals we conceded were disappointing, but I am not attaching blame to anyone. The first goal was particularly disappointing. We had a chance to clear the ball.
“If you watch it on TV, when their second goal went in, that was probably the most I have ever reacted to conceding a goal. It did feel like a real sucker punch.
“I am disappointed for all the fans. A point at home to Leeds would have been a good point.
“I am really pleased with what the lads have done, but it is a points business. When you are more fatigued it is harder to make the right decisions.
“I thought the substitution at half-time changed it. He (Tyler Roberts) caused us no end of problems.”
The only downside for Leeds was a potential scare late on when talismanic playmaker Pablo Hernandez was replaced after complaining of an injury problem.
Meanwhile, Bielsa revealed he is unsure whether Leeds will add to their options before Thursday’s transfer deadline, with the club still keen on recruiting Swansea City winger Daniel James.
The Argentinian observed: “I do not have any certainty about welcoming a new player. If we can welcome players who are better than our players, as long as they are better than our players, then it would be good.”
Warne will intensify his own efforts to add to his squad with his attempts to bring in a striker before Saturday’s game put on hold by the player’s club.
The move will be revisited today, Warne confirmed.
Hull City’s play-off hopes took a dent in a 3-0 loss at Blackburn Rovers, the Tigers’ first defeat in 11 league matches.