The home side went 2-0 up after just 25 minutes thanks to goals from Phil Foden and Josko Gvardiol, only for Leeds to make it 2-2 in the second half.
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Foden then snatched the win in added time to send Man City into second, six points off current league leaders Arsenal.
Haaland, 25, was largely anonymous throughout the game, having the least number of touches of any outfield player who played the whole 90 minutes with 25.
After the game, Guardiola and his big Norwegian striker were spotted having what appeared to be a tense post-game debrief.