Daniel Farke's side went into the contest without a single defeat at Elland Road all season and they dominated large portions of the game in Yorkshire.
However, a late Sammie Szmodics goal - his 24th in the league this season - proved to be the difference, catapulting Rovers six points clear of the bottom three.
As for Leeds, they remain in third position in the standings, one point adrift of each of Leicester City and Ipswich City who have played a game fewer.
Leeds controlled the match during the early stages, only being denied the lead through Aynsley Pears producing a save to keep out Wilfried Gnonto's 20-yard strike.
Ethan Ampadu and Ilia Gruev also failed to hit the target with efforts of their own, before Pears kept out a strike from Connor Roberts.
Blackburn went 40 minutes without having a single shot on goal, yet that changed five minutes from the break as Sammie Szmodics's strike was kept out by Illan Meslier after Crysencio Summerville had been dispossessed on the halfway line.
Needing to up the ante, Leeds predictably went back on the offensive after the restart, Gnonto going closest with a shot that just missed the target.
However, Blackburn remained a threat on the break and came agonisingly close to going ahead, Roberts having to clear off the line at the back post with Tyrhys Dolan about to convert from close range.
Daniel Farke opted to ring the changes, introducing Sam Byram, Daniel James and Patrick Bamford, and it helped give Leeds a second wind as the game entered the final quarter.
Bamford should have perhaps put the home side in front, rising highest to meet a cross, but the forward mistimed a header that went harmlessly over the crossbar.
Moments later came the sucker-punch that the home fans would have feared. A long ball was headed down by Sam Gallagher and subsequently hooked into the path of Szmodics by Dolan, and the division's top goalscorer did the rest with a cool finish past Meslier from the edge of the area.
While Leeds laid siege to the Blackburn goal in search of an equaliser, they failed to create another noteworthy chance, leaving Blackburn to celebrate a win that could be the difference between survival and relegation come the end of the season.