Souleymane Doukara was the man who the hosts owed the three points to, the striker firing in shortly before the hour mark.
It was harsh on Bristol City, who created far more openings than the hosts but were unable to apply the finishing touch to slip to a seventh defeat in their last eight meetings with Leeds.
For United, it was a morale-boosting end to a week that saw Sam Byram sold to West Ham United.
The victory also sets up Steve Evans’ men for not only Tuesday’s trip to Brentford but also the FA Cup fourth round trip to Bolton Wanderers next weekend.
Considering the play-offs appear way out of Leeds’ reach, progress against the Trotters is imperative to keep the season alive. And, even allowing for Bolton’s struggles, United will surely have to improve in the attacking stakes on what was a lacklustre effort against third bottom City.
The first half was a total non-event, the closest the crowd came to even a sniff of goal being when Ben Gladwin had a shot that was easily dealt with by Marco Silvestri.
Even then, it took a mistake by Liam Bridcutt on deep inside the United penalty area to gift possession to the visitors.
Otherwise, Gladwin also poked a cross from Joe Bryan wide and Jonathan Kodija did the same with another delivery from Luke Ayling in a 45 minutes that will not live long in the memory.
Kodija was also denied just before the break by Silvestri after making light work of Giuseppe Bellusci en route to the Leeds goal.
United’s lacklustre efforts were perhaps summed up by a move that saw Scott Wootton fire what looked to be a pass capable of releasing Souleymane Doukara only for the striker to take his eye off the ball as it hit him on the back of the head.
After being jeered off at the interval by the disgruntled home fans in a crowd of 20,441, the onus was on Leeds to improve and they did just that.
Evans’ decision to switch to 4-4-2 when bringing Chris Wood played a part, as it meant Doukara was in the middle to latch on to a 59th minute opening and fire past Richard O’Donnell.
Stuart Dallas, after exchanging passes with Wood, had provided the cross that the Robins had been unable to clear and the result was Doukara’s third strike in four games.
The visitors, under the charge of former Leeds defender John Pemberton as caretaker manager, almost replied straight away when a Marlon Pack corner evaded the home defence but Alex Pearce could only head over despite being unmarked.
Aden Flint was equally culpable ten minutes from time when heading wastefully wide after Freeman’s floated cross from the right wing had created the opening.
A swift counter attack then presented the visitors with another opening but Luke Ayling scuffed his shot to present Silvestri with a simple save.
Leeds head coach Steve Evans confessed: “The first half was like going to the dentist. It wasn’t pleasant and it was a long 45 minutes. It was a scrappy game. We were poor in quality all over the pitch in that first half - it was lazy and sloppy.
“I told them to find a moment of magic in the second half and they did that with Souleymane Doukara’s goal.”
Evans was full of praise for Doukara’s attitude on the field and in training. The Frenchman’s goal, driven in after City failed to clear a right wing cross from Stuart Dallas, was his third in four games and Evans said: “He is a player who needs to be loved and valued. He is getting the rewards for all the hard work he has put in.”
John Pemberton, City’s interim manager and former Leeds defender, was disappointed after seeing Aden Flint head wide of an open goal with 11 minutes left.
Pemberton said: “The one Aden missed near the end he would have buried last year.
“I was expecting the net to ripple and I couldn’t believe it when the ball went wide. We are disappointed with the scoreline because we didn’t deserve to lose, but we can get out of the trouble we are in. We have a stronger foundation now and are looking harder to beat.
“We probably need a bit more experience in the middle of the park and a bit more composure with our final ball, but I was at Leeds for four years so I know what it is like to play here. Some of my players were experiencing the mental test of playing at Elland Road for the first time.
“The result was a bitter pill to swallow because Leeds had one chance and scored from it. That is what happens when you are where we are in the table.”
Evans expects the transfer of Toumani Diagouraga from Brentford to go through over the weekend if the midfielder passes his medical.
“He was here today and we are just awaiting the outcome of his medical to complete the deal,” said Evans.