Marcelo Bielsa's side claimed an impressive three points against the Premier League's champions-elect.
The Whites went ahead through Stuart Dallas in the first half but were up against it following a red card for captain Liam Cooper after VAR intervened over a tackle on Gabriel Jesus.
Leeds defended deep in the second period and were finally undone through Ferran Torres as the wide man struck 14 minutes from time.
City again pushed on but it was the 10 men of United who burst through in stoppage time as Dallas slid home an unlikely winner to spark wild celebrations across the Pennines.
Here, we take a look back at the best pictures from a memorable afternoon for Leeds United in Manchester:
7. Leeds not happy
Diego Llorente and Tyler Roberts complain to referee Andre Marriner at half-time over his decision to reduce Leeds to 10 men just seconds before the interval. Photo: Getty
8. City fightback
With a man less Leeds are pushed back deep into their own half as City produce wave after wave of attack in the second period. Photo: Getty
9. Torres levels
Pressure finally tells on Bielsa's men as winger Ferran Torres levels after finding space in the area - could Leeds now hold on for a point? Photo: Getty
10. Pep frustrated
United hold firm as City go in search of a late winner. Guardiola is left frustrated by his sides inability to break Leeds down. Photo: Getty
11. Dallas scores again
The clock ticks into added time and Leeds break. Dallas latches onto a ball from Gjanni Alioski and slides home past Ederson... wild celebrations follow. Photo: Getty
12. Dallas at the double
What a goal and what a win. Dallas' late strike leaves no time for City to respond. Leeds have done it... Photo: Getty