Sammie Szmodics' double strike gave Blackburn a vital win as they marked the 5,000th league game in their history.
The midfielder scored in either half to keep Boro anchored to bottom spot with five defeats from six.
Matt Crooks gave Boro hope with a goal in an end-to-end game in which both teams missed a host of chances.
Rovers became only the seventh English club to play 5,000 league games, and moved up to eighth.
They celebrated by parading a string of past legends on the pitch, and EFL chairman Rick Parry presented the club with a commemorative trophy before kick-off.