Leeds now face second-placed Sheffield United at Bramall Lane next Monday (20:00 GMT).
A win would send them five points clear at the top of the Championship and potentially as many as 10 points clear of third place.
Farke was shown a yellow card by Stuart Attwell, his third of the season, in the bedlam that followed his side's winning goal.
It means the German will serve a one-game touchline ban for the short trip to South Yorkshire.
Sunderland, who are unbeaten at the Stadium of Light, host struggling Hull City on Saturday.
Leeds boss Daniel Farke told BBC Radio Leeds:
"These type of wins are the best kind you can have in football for the supporters and the whole group.
"They are priceless points. It's a great night for everyone connected to Leeds United.
"We haven't won anything yet but to do this against one of the best sides in the league in a difficult game.
"We were there with almost 70% possession so it was well deserved but once they led it is so difficult and complicated.
"I had only one yellow card before this season and now I have had a couple of doubtful ones.
"If I miss the game at Bramall Lane because of a celebration to a 95th minute goal then I have to adapt to the rules. We live by the rules but I doubt if it makes sense. It is what it is."