Wilfried Gnonto's 48th-minute goal earned a 1-0 victory that took them one point above third-placed Ipswich Town and nine behind runaway leaders Leicester City, though the Blues enjoy two games in hand and the Foxes one over Leeds.
The Italy winger beat goalkeeper Max O'Leary with a clinical left-footed finish from 10 yards after running on to a deflected long ball forward from Junior Firpo.
It was no more than Leeds deserved for a hugely impressive display in a largely one-sided contest, with their hosts out of sorts and only able to create a few openings.
Leeds should have won by a wider margin as they outplayed their mid-table opponents, but a mixture of Max O'Leary saves and some poor finishing kept City in the game.
Farke was delighted with the majority of his side's display but admits they will need to be more ruthless in front of goal if they want to secure promotion back to the Premier League.
"The margin of victory should have been greater. It was almost the perfect away performance," said Farke.
"We were so dominant and created so many chances, but I have to criticise our failure to put them away.
"If we want to be celebrating in May we have to be more clinical.
"We were breaking with three on one situations and not getting the final pass right over three yards.
"That has to change. But in all other respects I am so happy with the players."
City had one great second-half chance to equalise after 66 minutes when substitute Anis Mehmeti ran onto a Tommy Conway pass only to see his low shot saved at the second attempt by Illan Meslier.
But O'Leary made fine saves to deny the lively Crysencio Summerville on three occasions, as well as Georginio Rutter and Patrick Bamford.
The home side looked off the pace at times and head coach Liam Manning had no complaints.
He said: "First I have to give Leeds credit for being the best side we have played, but tonight we weren't at the level we are capable of.
"I am frustrated because I know we can be so much better. The players seemed to tense up after making errors.
"We have played the top sides and Leeds were the best. I expect them to sustain a promotion challenge."
