The 26-year-old got the solitary goal in the 19th minute of the encounter.
The former Nottingham Forest striker drilled home from Ashley Fletcher’s across to register his 12th goal in 32 appearances.
Moments before the half-time break, Blackburn were reduced to ten men after Derrick Williams was shown a straight red card following a harsh challenge on Fletcher.
Assombalonga featured for the entire duration of the game along with Nigeria international John Obi Mikel.
The victory saw Middlesbrough climb to the fifth spot in the log with 54 points from 32 games.
Boro will hope to continue the impressive form when they visit Queens Park Rangers on February 23.