Middlesbrough edged a narrow encounter at Ewood Park, with Britt Assombalonga's close range first half finish proving decisive.
Assombalonga nodded home from a couple of yards out to earn all three points for play-off chasing Rovers, who saw Derrick Williams sent off on the stroke of half time.
But the second half display probably warranted more for the efforts, with Bradley Dack coming closest to grabbing an equaliser towards the end of the game.
Tony Mowbray named four changes for the lunchtime clash, with Williams, Harrison Reed, Bradley Dack and Danny Graham all returning to the starting XI.
The quartet came in for Amari'i Bell, Lewis Travis, Richie Smallwood and Craig Conway, who were all available as substitutes against Boro.
The visitors started brightly, with Ashley Fletcher testing David Raya with a header after getting on the end of an expert cross from the right from Lewis Wing.
The next opportunity saw Boro take the lead, as Assombalonga headed home from a couple of yards out after Fletcher's deflected cross-shot floated into his path midway through the half.
Mo Besic's attempt from 20 yards was comfortable for Raya, with Rovers struggling to produce any sort of attacking threat.
The home side almost found an equaliser on the stroke of half time, when a whipped ball from Elliott Bennett found the head of Graham, but only great defending from captain George Friend stopped the frontman from testing Darren Randolph.
Things went from bad to worse for Rovers when the returning Williams was shown a straight red card for bringing down Fletcher on the edge of the box, and the resulting free kick from Wing was blocked well by Reed.
Such was Middlesbrough's dominance, Mowbray made all three changes at half time, with Bell, Travis and Ryan Nyambe all entering the action in place of Jack Rodwell, Corry Evans and Ben Brereton.
Just two minutes into the half and the impressive Wing clattered Raya's upright with a strike from all of 25-yards after the ball dropped to the 23-year-old.
At the other end, a teasing cross from Bell was almost guided into te back of his own net by Ryan Shotton, but the ball crept just inches past Randolph's right-hand post.
The hosts were growing into the game, and Dack glanced a header wide after connecting with an inviting Charlie Mulgrew free kick on the hour mark.
Soon after and Raya reacted well to flick over a Jonny Howson cross as the Teessiders looked to kill off any hopes of a Rovers recovery.
Graham spurned a glorious chance to level the score up with 13 minutes left, but after evading Shotton, he scooped over the bar with his left foot.
A moment later and Fletcher fired straight at Raya when through on goal as Rovers lived to fight another day and set up a grandstand finish at Ewood.
Randolph produced a spectacular stop to deny Dack with eight minutes left after the playmaker got on the end of Graham's excellent knockdown into the danger area, the Republic of Ireland international stopper sticking out a glove to stop the low attempt.
The game was opening up and substitute Stewart Downing curled just past the post as chances arrived for both teams.
Raya kept the hosts in it with a few minutes to go, stopping Assombalonga from completing his brace before flicking the ball out for a corner.
Rovers threw the kitchen sink at Boro right until the full time whistle, but ultimately came away disappointed and pointless against Tony Pulis' resolute Boro.
Rovers: Raya, Bennett, Rodwell (Nyambe, 46), Mulgrew (c), Evans (Travis, 46), Reed, Brereton (Bell, 46), Dack, Armstrong, Graham.
Unused substitutes: Leutwiler, Smallwood, Nuttall, Conway.
Booked: Rodwell, 33
Sent off: Williams, 45
Middlesbrough: Randolph, Mikel, Friend (c) (McNair, 61), Shotton, Assombalonga, Howson, Fletcher (Hugill 81), Fry, Saville, Wing, Besic (Downing, 73).
Substitutes: Konstantopoulos, Clayton, Hugill, Downing, Tavernier, van la Parra.
Goal: Assombalonga, 19
Referee: Darren Bond.
Attendance: 13,249 (1,052 away)