Kalvin Phillips hit the only goal of the game as Leeds edged past Birmingham 1-0 to move into the automatic promotion places.
Phillips opened the scoring on 65 minutes after the ball squirmed through Lee Camp to give the hosts a deserved win.
United, who have scored just five times in their opening six home games, had dominated the first half but were unable to trouble the Blues' defence.
But they did just enough in the second half against the lacklustre visitors to mark the club's 100th birthday celebrations in fitting fashion.
Camp unconvincingly palmed a Gjanni Alioski shot to safety on eight minutes as the home side enjoyed a good start and Marc Roberts did well to turn a cross behind for a corner on 14 minutes as Leeds turned up the pressure.
Lukas Jutkiewicz went into the book on 21 minutes for a late tackle on Stuart Dallas, before Alioski fired wide from the resulting free-kick
Patrick Bamford flashed an effort narrowly wide on 28 minutes from a tight angle.
Jutkiewicz fired wide during a rare Birmingham attack minutes later.
Helder Costa had a chance blocked after a superb back-heel from Bamford created an opening and Camp then parried the ball to safety after Dallas pounced on the rebound on 38 minutes.
Ivan Sunjic went into the book after going through the back of Alioski after he threatened to go on a run just before half-time.
Dallas was inches away from getting on the end of a Bamford pass deep into first-half stoppage time.
United brought Eddie Nketiah on for Bamford at half-time, with Nketiah having stated his desire to get more starting opportunities during the week.
The Arsenal loan man won a free-kick right on the edge of the box two minutes after the restart as Leeds appealed for a penalty.
Fran Villalba Rodrigo was not far away with a long-distance effort on 51 minutes, before Nketiah saw a long-range shot deflected straight to Camp.
Ben White made a brave block on 59 minutes to prevent Alvaro Gimenez from getting a shot away, before Jutkiewicz had a long-range shot saved.
Leeds finally found the opening goal when Phillips slotted the ball under Camp with the keeper knowing he should have done better.
Jack Harrison fired just wide before Alioski fired over the bar from close range as United went in search of a killer second goal.
Kristian Pederson headed over in stoppage time form a great position in stoppage time as Leeds held on.
What the managers said...
Marcelo Bielsa: "It was a really important match for us to win. I am not happy with how we closed the game out. After we scored we could have finished the match and we gave them the ball and let them control the chances. We have one of the best first halves we have played. We started the second half with some doubt and after the goal we had three chances to finish the match and from then little by little we allowed the opponent to control the ball. When they have the ball they will have chances to score.
"Sometimes God put things in the right place. Phillips is playing at Leeds and now he will stay in the history of the club for this goal. We were very focused on the match. The team showed that throughout the match in every moment. It was difficult for us to score in the first half, but it was a great performance. I am proud to have this job at a club with such important history. The history of the club is very impressive and that increases the duty I have."
Pep Clotet: "Apart from the high possession that Leeds usually have, our team had more shots than then, it was very even numbers. We knew it would be a difficult match ahead against a team that has been so good for a year and a half.
"We could sit deep and defend our box or take the game to Leeds, that is the game we did and I think we deserved more. We could not turn a very good performance into a result. I saw a lot of positive points."