Leeds United reaction: Thomas Christiansen expecting added pressure as Championship leaders
Samuel Saiz scored his sixth goal of the season in the first half and substitute Stuart Dallas eased frayed nerves by ramming home a low finish in the final minute.
Victory lifted Leeds top for the first time since the opening day of the 2004/5 season, while they last looked down on the second tier for more than 24 hours when Howard Wilkinson's side won the old Second Division title in 1990.
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Hide Ad"It's just a situation at the moment," said Christiansen, who admitted his players showed signs of fatigue as they extended their winning league start to seven matches and nine in all competitions.
"If you tell me it's the last game and we're in that position I would be happy, proud and all that you can say about that.
"But right now, don't give me anything. It puts a bit more pressure on the team because everyone now wants to beat Leeds.
"The performance was not the best, but if you still take the three points you have to be proud. What we have done until now is a high level."
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Hide AdBirmingham will feel aggrieved to have got nothing from the game. Their performance belied their poor start to the season and had most in a crowd of 31,507 praying for the final whistle as Leeds held on to their slender lead in the closing stages.
"I'm very happy with the result and also the way we took these three points. It was a very difficult game," Christiansen added.
"Birmingham gave us these problems, but when you manage to take the three points even when you play not so good, or the same performance as in the last game, then you're probably more satisfied.
"They didn't play to their best. It was obvious. We didn't control the situation as we wanted, but this is because we had a very good opponent."
Christiansen confirmed captain Liam Cooper is expected to be fit for Saturday's trip to Millwall after being forced off with a knock in the second period.