The Yorkshire giants went into Friday's contest at Loftus Road with the opportunity to move four points clear of third-placed Ipswich Town in the Championship standings.
Instead, Leeds would suffer their heaviest defeat of the campaign as the Hoops starved off any relegation fears with two goals in either half.
Ilias Chair and Lucas Andersen put QPR in control by the 22nd minute before Lyndon Dykes and Sam Field got on the scoresheet after the break.
While Marti Cifuentes and his squad were able to celebrate joyously with their supporters, Leeds were left to reflect on handing the advantage in the automatic promotion race to Ipswich.
What does QPR win mean for promotion race?
Leicester City were the main beneficiaries on Friday evening as the Foxes were confirmed as champions, but Ipswich now have the chance to take full advantage.
The Tractor Boys require a maximum of five points from their final three games to secure second place, those fixtures against Hull City, Coventry City and Huddersfield Town.
With Leeds not playing again until next Saturday, two wins for Ipswich on Saturday and Tuesday will earn the runner-up spot before Farke's team are back in action.
What did Farke have to say?
Although Farke was complimentary of QPR's victory in the capital, the German hinted that there were a number of factors why Leeds were so overawed in their most important game of the season.
Speaking to Sky Sports, Farke said: "First of all, congratulations to QPR. It's a well-deserved win for them and we have to accept the loss. Decisive for the game were the first 15 minutes. We were poor in this period, didn't win any duels.
"We speak a lot about principles, tactical approach but today the basics were not good. Moving enough and being compact as a team and winning duels. Then we were already 2-0 back.
"After that we started to play the game. Tried to put lots of pressure on their men. Then they scored two more out of set pieces. Then we had to make sure we don't concede any more. It's an off day today.
"The last two games we've conceded too many goals, today we've conceded too many goals. There are several reasons not excuses - quick turnarounds, key players missing, with a really young side they were perhaps a bit nervous or over motivated. All together they played a role.
"We know in terms of automatic promotion we are not in the best position now but this team has no reason to dwell on this really poor game today. With 90 points after 45 games, normally you win the league with this. It's not the right moment to feel too sorry for yourself. We have to keep going now."
Leeds have now only won one of their last five games in the Championship, that success coming by a 4-3 scoreline at Middlesbrough on Monday.