Connor Roberts, Archie Gray and Patrick Bamford all struck for Leeds in the final ten minutes after Wout Faes' first-half header had put leaders Leicester in front.
Farke's side equalled a 92-year club record of nine straight league wins and extended their unbeaten run at Elland Road this season, while the German is the first Leeds manager to remain undefeated in his first 19 home games in charge.
The former Norwich boss, whose side have cut the gap on Leicester to six points after trailing them by 17 at the turn of the year, said: "It's a great evening for everyone connected with Leeds United.
"To be there with a ninth win in a row, unbeaten here at Elland Road this season there are many record-breaking statistics.
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