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: