The German’s tactical switch at half-time saw the Whites come from 2-0 down to level before man-of-the-match Phil Foden arrowed in a classy winner in the 91st-minute.
It was Foden who got City up and running in the first minute. Leeds have conceded many goals down their left flank so Farke brought in James Justin, for his full debut, and Willie Gnonto for regulars Noah Okafor and Gabriel Gudmundsson.
The result was the same, a cross from the left, this time by Mateus Nunes, converted by a midfielder in the box.
It went from bad to worse as Josko Gvardiol knocked in the second on 24 minutes after Leeds failed to deal with a corner.
Despite some heroic last-gasp defending, United were putting in a display that could get their manager a P45. They were passive and tentative. City should have been out of sight by the interval.
Farke removed his wingers at half-time and sent on an extra defender in Jaka Bijol and added striker Dominic Calvert-Lewin to go 5-3-2.
Farke said: “I was not happy with our execution and we changed our structure in possession to have more control and passing angles against their pressing.
“We got more and more control and belief. The lads showed a fantastic second half, fully deserved the equaliser.
“I think both teams could have won it.”
The match became a different game after his tactical switch. Within four minutes of the restart Calvert-Lewin took advantage of some poor defending by Matheus Nunez to pull one back.
City were rattled. Leeds started to make most of the running with Calvert-Lewin a handful. It needed streetwise goalkeeper Gianluigi Donnarumma to go down with a mystery injury - an incident with irked Farke - to enable Guardiola to give his team a touchline “Pep” talk.
The worried City chief’s message didn’t initially sink in as Gvardiol took out Calvert-Lewin in the box, Lukas Nmecha netting the 68th minute rebound equaliser after Donnarumma saved his spot-kick.
Leeds continued to press high up the pitch but gradually City regained control in the later stages.
After a stray Ao Tanaka pass was picked off, City kept possession before Foden fired unerringly through a crowd of players into the bottom corner to undo all United’s good work in the second half.
Although it was a sixth defeat in seven, there were many positives for Leeds to take from the second half - not least keeping goal-machine Erland Haaland off the scoresheet as he sought his 100th Premier League goal.
Although 3-5-2 brought a vast improvement in United’s second-half performance there is no guarantee the formation will be repeated when Leeds take on Chelsea at Elland Road on Wednesday night.
Farke said: “It has to fit to a game, to a structure. How Man City played today, the way they pressed, for that it was right.”