The game will not live long in fans’ memory, but it was all about the points with the Whites now pulling 11 points clear of their third from bottom opponents.
The goal was their only effort on target, but it was enough to make it six matches unbeaten at home and Leeds are back up to 16th in the SkyBet Championship.
Little happened from an attacking sense in a desperately poor first half as United struggled to create opportunities with Doukara on his own up front and Lewis Cook struggling to get into the game in his attacking midfield role.
It summed up Leeds’ first half display when they won a free-kick 25 yards out only for Mustapha Carayol to fire hopelessly over.
The only other effort was a weak header by Stuart Dallas from a rare decent cross by Charlie Taylor.
Bristol City were a little better as Ben Gladwin had a near post shot saved by Marco Silvestri and Jonathan Kodija sent a header just wide.
Gladwin also went close with a near post volley while quick footed striker Kodija worked his way into the box only to be denied at close range by Silvestri and it remained goalless to half-time.
To show what kind of game it was when the board went up for two minutes added time it brought boos from the crowd who had seen enough.
The second half was livelier and Leeds showed more attacking intent with Doukara failing to make much contact with a glancing header after meeting an inviting cross.
Leeds boss Steve Evans sent on Chris Wood, back after injury, on 54 minutes to play two up front and immediately the team looking more likely to score with Doukara now adopting a more free role and Cook moved to the left wing in place of the disappointing Carayol.
The winning goal came on 59 minutes when Dallas’s cross bounced off Wood in the box and fell nicely to Doukara who supplied a calm finish, low into the bottom corner of the net.
The visitors almost equalised straight away when they won a corner and Alex Pearce was given a free header, but he sent it over the bar.
City had another chance with a header 11 minutes from time only for Aden Flint to send the ball wide when it looked easier to score.
Leeds then settled down and saw the game out, although they had one alarm as their opponents caught them short in numbers at the back on a swift breakaway, but Luke Ayling’s weak shot was easily saved by Silvestri.
United boss Evans admitted his side had been nowhere near the best.
He said: “The first half resembled a wait in the dentists.
“It was a scrappy. No question about the desire and effort to win, but we were poor in quality.
“I thought the first half performance at Sheffield Wednesday was outstanding and we could have been three goals ahead. So the plan was to reproduce that in the first half today, but we looked a yard off all over.
“I could not repeat the words I had at half-time. The clear instruction was we had to grind our way into the game and find a bit of magic, which we did.
“We weren’t at our best today, but we got our rewards after a good display last week.
“I thought I would only get 30 minutes out of Chris Wood and he did well when he came on.
“He played a part in the goal and Souley put the ball in well. I thought he put a big shift in for us last week and he was one of the better players in the first half.
“Doukara I identified early as someone you need to love and we’ve worked on that. He’s now getting the rewards for working hard.”
Leeds United 1
Bristol City 0
Saturday, January 23, 2016
Sky Bet Championship
Leeds: Silvestri, Wootton, Bellusci, Cooper, Taylor, Dallas, Bridcutt, Murphy (Adeyemi 90), Cook, Carayol (Wood 54), Doukara (Antenucci 86),
Bristol City: O’Donnell, Ayling, Flint, Baker (Pearce 45), Bryan, Burns, Smith, Pack (Wilbrahim 77), Gladwin (Reid 61), Freeman, Kodija.
Referee: Charles Breakspear