Marcelo Bielsa on 'strange match' as Leeds United go top after nine-goal thriller
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A great start saw the Whites two up just past the 20 minute mark only for Birmingham to hit back to level with goals either side of half-time.
Once again Leeds appeared in control at 3-2 then 4-3, but their inability to defend crosses left them vulnerable and when Lukas Jutkiewicz netted his second in injury-time it looked as if two points had been thrown away only for an even later winner to come from a forced own goal by Wes Harding.
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Hide AdBielsa admitted it had been a heart stopping match in which so much about his team had been turned on its head.
Where they have been solid in so many other games they looked all over the place at the back at times while they scored five goals from only five efforts on target.
The Leeds boss said: "All the previous analysis about our team, we saw the opposite in the match.
"We had high efficiency to score and we are a team that needs a lot of chances to score.
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Hide Ad"We didn't have safety in defence. We have conceded goals that normally we would think we're in good condition to avoid.
"We should have controlled the match better in the first half.
"It was difficult for us. In the first part of the second half the match had no definition, even though we improved in this period.
"After 2-2 the match was strange. It was goal for goal. The spirit of the team when Birmingham pulled it back 4-4, Alioski was playing as a left winger, trying to score to make it 5-3. Every time when Birmingham scored we had energy to go for one more goal.
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Hide Ad"After we have to analyse, as we analyse every match, correct what we need to improve, try to see what we did well as well."
Bielsa added: "Of course I would like to try to control the match when we are winning and not just control the match to win the match.
"When the opponent protects itself we play better. But when the opponent needs to score it is difficult for us to control the match."
The glee at the injury-time winning goal was added to as it put United back on top of the Championship with West Brom suffering their first home defeat of the season - just ahead of their New Year's Day game at home to Leeds.
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Hide AdIt looked like a routine afternoon for the Whites early on as a team with Eddie Nketiah up front in place of the injured Patrick Bamford scored their two early goals.
The first was a superb break in which Jack Harrison came up with a great run and pass to set up Helder Costa, who was equally impressive with his crisp finish.
Harrison turned scorer six minutes later after his shot went in via a deflection following another well crafted move.
It was a surprise when Birmingham pulled a goal back just before the half-hour as Jude Bellingham was allowed freedom in the area to pick his spot after finishing off a Maxime Colin cross.
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Hide AdThis was the cue for the hosts to have their best spell of the game as Jutkiewicz volleyed over a good chance, but they were still behind at the break.
Leeds held their opponents at arm's length in the early stages of the second half, but their usual controlled football was not there and their paid the price with a City equaliser round the hour mark.
A far post corner was not dealt with and an under pressure Kiko Casilla could not get any distance as he aimed to punch clear with Jutkiewicz heading home the rebound from close in.
A crazy finish to the match followed and resembled a kids game with a 'we score, you score' feel about it.
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Hide AdLeeds went back in front with a superb volley by Luke Ayling from the edge of the box after he had collected an equally impressive crossfield ball by the other full-back, Ezgjan Alioski.
But the next set piece to defend brought a third Birmingham goal as Casilla came rushing out to meet a free-kick, but did not get to the ball as it was headed in by Jeremie Bela.
The responce was swift this time as less than a minute later United went straight down the other end and Stuart Dallas was found in space in the area by Ayling and finished smartly to make it 4-3.
Still it was not over as Bela's cross caught the visiting defence out and Jukiewicz finished at the far post to level it up once more.
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Hide AdThere was one final twist, however, with Costa and Ayling combining well down the right for Leeds and the latter's driven low cross turned into his own net by Birmingham defender Harding.
Match facts
(Bellingham 27, Jutkiewicz 61, 90+1, Bela 83)
(Costa 15, Harrison 21, Ayling 69, Dallas 84, Harding 90+5 og)
Championship
Attendance: 22,059
Birmingham: Trueman, Harding, Pedersen, Colin, Crowley (Bela 68), Jutkiewicz, Dean, Mrabti (Gimenez 74), Gardner, Bellingham (Montero 74), Sunjic.
Subs: Camp, Bela, Montero, McEachran, Maghoma, Gimenez, Davis.
Leeds: Casilla, Ayling, White, Cooper, Alioski, Phillips, Dallas, Klich (Berardi 86), Harrison, Costa, Nketiah (Roberts 81).
Referee: Keith Stroud.