Marcelo Bielsa's outfit toppled the Canaries on Sunday afternoon in Premier League action thanks to a hard-fought 2-1 win in Norfolk.
United secured only their second three-point haul of the campaign and earned a first victory away from home against City.
Leeds weren't at their free-flowing best against their relegation-threatened hosts but bagged two goals in a frantic five-minute second half spell to take all the spoils.
Brazilian winger Raphinha opened the scoring after the half-time interval with a fine solo run into the box, finishing off low past goalkeeper Tim Krul after gliding past three defenders to find the back of the net.
The Canaries, though, restored parity just 120 seconds later through Andrew Omobamidele's glancing a header off the underside of the crossbar.
Leeds then lifted themselves back in front once more through Rodrigo as the Spaniard saw his well-hit shot from distance sneak under the outstretched hand of Krul and into the bottom corner.
Daniel Farke's men pushed on again but it was Leeds who controlled the affair thereafter to send the travelling fans back to West Yorkshire happy.
Rodrigo made it two goals in two games after last week's converted penalty against Wolves and was left brimming at the full-time whistle post-match.
"It was a very important goal. I think we needed victory," the match-winner reflected at full-time.
"We haven't started the season well, but it's true that we deserve more than we have now. I'm happy with my goal but more so for the win.
"We are a team that tries to command the game, we have this style. Sometimes because of this style, we concede something to the opponent.
"We dominated the game and deserved the win and the team was congratulated for it. It is more than three points; we played against a team who is having a bad moment, like us.
"It is a really important result and we are now looking forward to the next game [against Leicester City]."
Asked about the belief in the dressing room amid a number of senior injuries, Rodrigo added: "It's true we had some injuries in the last games. We still have some important players out like Pat [Bamford] and Luke [Ayling].
"But this is the strength of the squad. We all prepare for everything. We are really happy for the win today."

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