Polish striker Jutkiewicz struck for the second successive game with a clinical low finish from the edge of the penalty area to lift Tony Mowbray's side up to third, within a point of second-placed Hull.
Blackburn, who have now won only once under manager Henning Berg in 10 matches, were made to pay for missed chances and continue to slide down the table after securing just one point from their last six fixtures.
Rovers' late substitute Ruben Rochina was denied a late equaliser when Middlesbrough goalkeeper Jason Steele kept out his free-kick, but the home side were also guilty of some wasteful finishing.
Middlesbrough made the brighter start as Jutkiewicz and Ledesma both fired over the crossbar from inside the penalty area before 16-goal Blackburn striker Jordan Rhodes fired a shot just off target at the other end.
Rosado then tested Steele with a swirling, angled drive from 35 yards that was well held by the Boro goalkeeper and in a see-saw opening Jutkiewicz's header from Ledesma's cross was gathered by Blackburn goalkeeper Jake Kean.
Middlesbrough defender George Friend and midfield team-mate Grant Leadbitter both fired in shots from outside the area, but the home side were given a let-off in the 24th minute when Rhodes spurned a gilt-edged chance from close range.
Boro continued to rain in shots from long range. Rosado, again from more than 30 yards, striker Scott McDonald and Ledesma all tried their luck from distance before the break, but the score remained goalless at the interval.
Jutkiewicz was next to waste a golden opportunity when he headed wide from six yards from McDonald's telling cross in the 50th minute, while Rovers striker Colin Kazim-Richards saw his header saved by Steele before blazing the rebound over the crossbar with the goal at his mercy.
Jutkiewicz dragged an angled shot wide and forward team-mate Marvin Emnes arrowed a 25-yard effort off target, but in the 67th minute Boro broke the deadlock.
McDonald pulled the ball back towards the edge of the penalty area from the left and Jutkiewicz buried a low, right-footed shot into the bottom corner for his seventh goal of the season.
Blackburn boss Berg replaced Rosado with David Dunn in the 78th minute before fellow midfielder Jason Lowe fired a low angled shot just wide and moments later visiting goalkeeper Kean denied Boro a second when tipping McDonald's close-range effort over the crossbar at full stretch.
Rovers almost snatched a point in the final minute, but Rochina's goalbound free-kick was brilliantly saved by Boro keeper Steele.