Mateo Joseph and Joel Piroe scored second-half goals to hand the Whites a second successive win and condemn the Tigers to their maiden loss of the campaign.
Joseph neatly turned in a left-wing cross from debutant Manor Solomon at the near post in the 63rd minute before substitute Piroe finished coolly nine minutes from time from Junior Firpo's cross.
Those second-half strikes in an entertaining Yorkshire derby ensured Farke's men made it four leagues games without defeat and followed last Friday's 2-0 win at Sheffield Wednesday.
Farke said: "We spoke about a perfect away performance at Sheffield Wednesday and that feels like a perfect home performance. It's never that easy when you have so many incomings, but I'm really hap py.
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