Marcelo Bielsa made two changes from the defeat to West Brom as both Bailey Peacock-Farrell and Pontus Jansson were sidelined with injuries.
Goalkeeper Will Huffer and central defender Aapo Halme were both handed their first-team debuts by the Argentine as the Whites were down to the bare bones calling on the Under-23s to provide cover.
The opening 15 minutes passed without incident as Kalvin Phillips came closest to breaking the deadlock with a shot from outside the area but his effort flew high and wide.
It was Leeds though who pressed on as Gjanni Alioski forced Niki Maenpaa into his first action of the afternoon in the City goal as he tipped a drilled shot over the bar following a lovely dinked ball across the area from Mateusz Klich.
The visitors themselves opened up United for the first time minutes later as Jamie Paterson lifted the ball over the defence for Andreas Weimann but his low cross was collected with ease by Huffer after a nervy start from the Whites stopper.
As the half progressed it was Lee Johnson's team who settled the better but United again had another golden opportunity to grab first goal.
City were caught in possession as they played out from the back with Hakeeb Adelakun guilty of a stray pass which found Klich who fed in striker Kemar Roofe but his deflected effort fell the wrong side of the post in agonising fashion and it was as close as the two teams would come before the break.
The second period began in much the same vein but was sparked into life after 10 minutes as City midfielder Josh Brownhill was given his marching orders as he picked up a second yellow card for a foul on Roofe on halfway.
Leeds responded to the incident as Roofe fired an effort wide before some lovely build-up play from Adam Forshaw and Klich resulted in City throwing themselves at an Alioski shot.
Bielsa subbed on Jack Harrison and Samuel Saiz as United went in search of three points.
The Manchester City loanee made an immediate impact as he found himself alone in the area but he took one touch too many before getting a shot away as City recovered to block.
Barry Douglas then tested Maenpaa's hands from distance before Leeds finally had their goal.
Harrison drilled the ball low to the edge of the area as Pablo Hernandez dragged his shot into Roofe's path with the striker on hand to prod home from close-range to send Elland Road into ecstasy.
United went close again as Lewis Baker stepped off the bench to link up with Harrison with the former drilling an inviting ball across the face of goal but there was no-one in place to meet the ball with the goal gaping.
Leeds though weren't going to be denied a second as Bielsa's two tricky Spaniards linked up with Saiz lifting a lovely ball into the area for Hernandez to nod past Maenpaa in what was an identical goal to the consolation at the Hawthorns two weeks ago.
The strike was enough to wrap up all three points as United moved up to second in the league table firmly in the hunt for promotion just two points from leaders Norwich City.
Leeds United XI: Huffer, Halme, Phillips, Cooper, Dallas, Forshaw, Douglas, Klich, Hernandez, Roofe, Alioski. Subs: Miazek, Davis, Clarke, Shackleton, Baker, Harrison, Saiz.
Bristol City XI: Maenpaa, Webster, Brownhill, Weimann, Adelakun, Kelly, Eliasson, Paterson, Pack, Kalas, Hunt. Subs: O'Leary, Pisano, DaSilva, Baker, Diedhiou, Walsh, Eisa.