Tony Mowbray’s Boro were without a point on their travels in three attempts this season but took an early lead when the recalled Jutkiewicz was played in by Marvin Emnes.
Rovers - top of the Championship and unbeaten before tonight - scarcely fashioned an opportunity of note in the first half, although Fabio Nunes’ cross hit the crossbar in stoppage time.
Mustapha Carayol, who had a shot cleared off the line in the opening minute of the second period, then found Jutkiewicz just after the hour mark to head Boro’s second.
That brought the regular chants of "Kean Out" to a crescendo and a stoppage time goal from substitute Grant Hanley, amid a valiant late rally, could not prevent further barracking at the final whistle.
Blackpool, Brighton, Hull and Cardiff can all replace Blackburn at the Championship summit with a positive result on Saturday, while Boro edged into the play-off places.
Veteran Portuguese striker Nuno Gomes was restored to Blackburn’ s line-up having come off the bench to score the winner against Barnsley in midweek, his fourth in as many games.
Nunes and Bruno Ribeiro started in the wide attacking positions, while Gael Givet returned at centre-back following a dead leg.
Jutkiewicz replaced Ishmael Miller in Mowbray’s only change to the side thrashed 4-1 at Blackpool on Tuesday.
And it took only six minutes for him to justify his selection, collecting Emnes’ return pass from his own flick-on to slot beyond Paul Robinson at the near post.
Boro's set plays were unsettling Rovers and Grant Leadbitter almost curled directly into the far corner from the left flank with Robinson grasping at fresh air midway through the half.
Blackburn were restricted to the point that a speculative 30-yard drive from centre-back Scott Dann was their first shot on target in the 26th minute.
Nuno Gomes provided eye-catching touches when involved but Josh McEachran, Kevin Thomson and Leadbitter were overrunning Rovers in midfield, where Dickson Etuhu’s distribution was particularly erratic.
A scarcely deserved equaliser nearly arrived in first-half stoppage time when Nunes’ whipped left-wing delivery grazed the crossbar.
Boro almost increased their advantage a minute after the restart. Carayol burst in off the left flank to fire goalwards from an acute angle, forcing Martin Olsson to hack off the line after Robinson took the pace off the shot.
Carayol was the provider when Middlesbrough made it 2-0, drifting infield to clip a excellent ball to the far post for the unmarked Jutkiewicz to steer a superb header home.
Blackburn drove forward in response to growing discontent in the stands but were restricted to half chances as Andre Bikey produced a vital challenge to deny Jordan Rhodes.
A third Middlesbrough goal almost arrived in comical fashion when Bradley Orr’s clearance rebounded off Thomson and past the post with Robinson stranded.
Hanley, on for the injured Olsson, handed Rovers an injury-time lifeline by heading home Nunes’ cross when a free-kick was partially cleared, but Boro held on under frantic, sustained pressure.