Joe Rodon and Brenden Aaronson struck the goals for Leeds at Elland Road.
Farke said afterwards: "First of all, I'm delighted to take the three points. It is difficult to explain how we were standing there after the last three games with one point. We had much more domination and controlled the performance. We had a difficult week, in terms of illnesses and injuries.
"It was a difficult week for us. You could feel it. We showed passion and bravery.
"In the last 20 minutes you could feel it was a difficult week. A big fighting spirit, will and passion to bring it over the line.
"It is good for confidence to bring it over the line. A priceless three points.
"Of course, we spoke about set-pieces. We spoke about a few things we wanted to explore.
"Today we had to be smart in terms of our game management. They prepared to give all our energy today. Overall, the lads dug in and stuck together. A lot of fighting spirit today and we earned the three points."