Tony Mowbray's men were full value for the 2-0 win as Rovers never got going at Ewood on Friday night.
The visitors set the tone on the night after just seven minutes when Lucas Jutkiewicz exchanged passes with Marvin Emnes before lashing low past Robinson.
Middlesbrough continued to force the pace, pinning Rovers back for long spells, but it wasn't until the hour mark that the second arrived, Jutkiewicz having far too much room to head home his second from Carayol's cross.
Grant Hanley's 89th minute goal reduced arrears and sparked a frantic finish to the game as Jordan Rhodes had a strong shout for a penalty in added time, but despite plenty of pressure in the final moments 'Boro held on to claim all three points.
With this being the third game in six games it came as no surprise that manager Steve Kean made four changes from the side that defeated Barnsley on Tuesday.
Gael Givet returned to the centre of defence after injury replacing Grant Hanley, Bruno Ribeiro was preferred to Mauro Formica on the right, whilst the duo who combined for the midweek winner - Fabio Nunes and Nuno Gomes returned to the starting eleven with Morten Gamst Pedersen and Ruben Rochina dropping to the bench.
Rovers went into the game looking to stretch their unbeaten run to seven games, but the visitors hadn't read the script.
From the off they looked the livelier of the two sides and their seventh minute opener was just rewards for Tony Mowbray's side.
A hopeful ball forward caught Gael Givet under it's flight and as Lucas Jutkiewicz fed Marvin Emnes the Dutchman intelligently fed the ball back to Jutkiewicz and he beat Paul Robinson at his near post to put Middlesbrough in front.
Rovers were struggling, Middlesbrough giving the home side no time on the ball leading to passes going astray on many occasions.
Aside from dangerous crosses into the box from Bradley Orr and Fabio Nunes it was the visitors who continued to threatened.
At the midway point of the half Grant Leadbitter almost netted from a free-kick on the left, the midfielder's looping ball into the area was missed by Robinson but fortunately it missed the far post by a whisker.
Moments later Leadbitter was presented another chance after being teed up by the lively Jutkiewicz, but he blazed high over the bar.
Rovers' first shot on target arrived on 26 minutes and it came from the unlikely figure of Scott Dann, the defender advancing to shoot from 35 yards but Jason Steele claimed easily.
The home side continued to struggle as the first half drew to a close with Jordan Rhodes and Nuno Gomes starved of service, Fabio Nunes looking the liveliest in a blue and white as his cross shot grazed the crossbar in added time.
Mauro Formica was introduced at the start of the second half replacing Bruno Ribeiro but it was the visitors who once again started well.
Just two minutes in and Mustapha Carayol found it all too easy to get round the back of the Rovers defence, the wideman shot hard and low from an acute angle and although Robinson got a hand to the ball it needed the quick reactions of Martin Olsson to clear the ball off the line.
That would prove to be the last action for the Swede as he limped off moments later to be replaced by Grant Hanley.
Unlike on Tuesday when Barnsley didn't get a second goal when on top, Middlesbrough didn't have as much difficulty. Just past the hour mark the visitors doubled their lead when Mustapha Carayol sent over a ball to the back of the area where Lucas Jutkiewicz was there to score his second goal of the game with a looping header back beyond Robinson.
The second goal finally prompted a long-awaited response from Rovers. Dickson Etuhu fired over from Nuno Gomes' lay-off, then Jordan Rhodes saw his shot blocked by Andre Bikey.
Then from a Danny Murphy free-kick Scott Dann headed powerfully at the back post but his downward effort was claimed on the line by Steele.
Despite that brief rally it was the visitors who still posed the greater attacking threat. Paul Robinson having to beat away a fierce free-kick from Emnes before a clearance from Bradley Orr struck Leadbitter and rebounded just past the post.
Then with three minutes to go Carayol was denied once more by Robinson who then made it a vital double save to deny Emnes on the follow-up.
Jonathan Woodgate was a real rock at the back for Middlesbrough and suddenly following his substitute Rovers were in the ascendency.
With a minute left on the clock Rovers grabbed an unlikely goal to set up a frantic finish. Fabio Nunes, arguably Rovers' best player on a disappointing night, crossing for Grant Hanley and the young Scot headed home from six yards.
Suddenly it was the visitors with their backs to the wall. Rovers had to settle for a corner kick and not a penalty kick after Jordan Rhodes appeared to be fouled by Justin Hoyte in the area.
From the resulting corner kick Paul Robinson came up to add more threat, but as the ball arrived at the feet of the Rovers' 'keeper he scuffed his effort wide.
Rovers threatened again from another kick, but despite the best efforts of Etuhu, Orr, Hanley and Formica, Middlesbrough somehow kept the home side at bay.
Had Rovers grabbed an equaliser it would have been harsh on Tony Mowbray's side as they were the better throughout and were full value for their victory.
ROVERS: Robinson, Orr, Dann, Givet, Olsson (sub Hanley 49 mins), Ribeiro (sub Formica 46 mins), Etuhu, Murphy (c), Fabio Nunes, Nuno Gomes, Rhodes.
Subs not used: Kean (GK), Lowe, Dunn, Pedersen, Rochina.
Goals: Hanley 89 mins.
Booked: Olsson, Givet.
MIDDLESBROUGH: Steele, Hoyte, Bikey, Friend, Leadbitter (sub Bailey 88 mins), Thomson, Emnes, McEachran, Jutkiewicz, Carayol (sub Zemmama, Woodgate (c) (sub Hines 84 mins).
Subs not used: Leutwiler (GK), Ledesma, Arca, Williams.
Goals: Jutkiewicz 7, 61 mins.