After being frustrated for the most of the first hour the Whites ran out convincing winners following a red card shown to City midfielder Josh Brownhill for a second bookable offence.
From that point it was all Leeds and had they been sharper up front they could have won by a much bigger margin.
As it was the result gave United the bounce back victory they needed after losing 4-1 at West Brom and Bielsa was understandably pleased with the result.
They achieved it with a goalkeeper in Will Huffer making his senior debut and with rookie centre-half Aapo Halme also in the starting line-up for the first time.
Elsewhere, Bielsa went for a more conservative formation with two defensive midfielders in Adam Forshaw and Kalvin Phillips until the strings were cut and the game opened up after the break.
He said: “We didn’t concede virtually any chances, as far as I know, I don’t remember any situation like that.
“It’s difficult to think that we deserved to lose the game.
“The fact we played with one more made it easier for us, but that was not the only argument.
“We had a defensive structure that prevented any danger.”
Bielsa could not confirm that rookie keeper Huffer would play again in the next game as the extent to the injury to first choice Bailey Peacock-Farrell was not yet known.
Bristol City manager Lee Johnson felt the sending off changed the complexion of the game.
“He said: “I was pleased with the way we played and the shape. I thought we were going to go on and win, but the red card changed the game.
“We have had a few decisions go against us in recent weeks.
“Josh gave the referee a decision to make (with the second foul) and he didn’t see him slip.
“Leeds are a good side, but we nullified them up to that decision. I thought they were lucky today. I know they had a couple of players out and we didn’t work the goalkeeper enough, but sometimes when your luck’s in, your luck’s in.”
Bielsa will now be hoping the way his side finished the game they can take into the start of Tuesday’s back to back home game against Reading.
They then face a huge Yorkshire derby next Saturday lunchtime when away to promotion rivals Sheffield United who will present Leeds with a big challenge and are battle hardened in the derbies after draws with Sheffield Wednesday and Rotherham United in recent weeks.
It took Leeds 18 minutes for their first decent effort on goal against Bristol City with Ezgjan Alioski seeing a volley from inside the area tipped over by keeper Niki Maenpaa.
The visitors threatened from set pieces with Tomas Kalas heading wide from a corner and Lloyd Kelly forcing Huffer into his only save, aside from dealing with crosses, a comfortable catch from a header.
Huffer did have one escape as his attempted punch clear from a free-kick landed straight to Jamie Paterson on the edge of the box, but he volleyed over.
Leeds had a good opening when Mateusz Klich ran into the box, but for some reason did not to choose to shoot, trying to play Kemar roofe in, instead. Roofe then saw his effort from a more difficult angle deflected wide and the first half ended goalless.
City showed more intent at the start of the second half with the game opening up. Niclas Eliasson saw his shot deflected onto the roof of the net and Hakeen Adelakun intercepted a poor pass by Phillips only to hit his 20-yard shot over.
It all changed in the 55th minute, however, with Brownhill receiving his second yellow card for a tackle from behind when he missed the ball. Having already been booked it was a poor challenge to come up with and he received his marching orders.
Before the visitors could reorganise they were suddenly being overrun as wave after wave of Whites attacks came.
Alioski volleyed over then Roofe was clean through from Phillips’ quick pass, but from an angle shot narrowly wide.
Alioski was well set up in the area only to fail to get a shot away and his cross was blocked for the good chance to be wasted.
Klich then saw his 25-yard shot comfortably saved and substitute Jack Harrison was the next player to take too long to get a shot away after being given an opening in the box.
Barry Douglas saw his well struck shot from range superbly tipped away by Maenpaa before the goal that looked inevitable at this stage came. It had some luck about it as Pablo Hernandez’s shot did not look likely to trouble the keeper, but Roofe nipped in to divert the ball in from close range.
Leeds doubled their advantage three minutes from time with a goal made in Spain when substitute Samuel Saiz picked out Hernandez and he beat Maenpaa with a header that floated into the far corner of the net for his sixth goal of the season.
The Whites comfortably saw out the remainder and could have added another in added time as third sub Lewis Baker’s shot from distance was saved by Maenpaa.
Leeds United 2
(Roofe 69, Hernandez 87)
Bristol City 0
Saturday, November 24, 2018
Sky Bet Championship
Leeds: Huffer, Dallas, Halme (Saiz 64), Cooper, Douglas, Phillips, Forshaw, Hernandez, Klich Baker 82), Alioski (Harrison 61), Roofe.
Bristol City: Maenpaa, Hunt, Kalas, Webster, Kelly, Eliasson (Diedhiou 61), Pack, Brownhill (Sent-off 55) Paterson (Eisa 78), Adelakun (Walsh 61), Wiemann.
Referee: Scott Duncan.